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1/2 + 1/4 + 1/8 + 1/16 + ⋯. First six summands drawn as portions of a square. The geometric series on the real line. 16 + is an elementary example of a geometric series that converges absolutely. The sum of the series is 1. Has been rising the past three years, climbing 2.4 percent in 2013, 4.4 percent in 2014 and 0.8 percent in 2015. This increase of more than 7 percent over the past three years places an unusual upward pressure on claim costs. It appears the immediate reason claim frequency is rising is that people are driving more miles.

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The MySQL installation process involves initializing the data directory, including the grant tables in the mysql system schema that define MySQL accounts. For details, see Section 2.10.1, 'Initializing the Data Directory'.

This section describes how to assign a password to the initial root account created during the MySQL installation procedure, if you have not already done so.

Alternative means for performing the process described in this section:

• On Windows, you can perform the process during installation with MySQL Installer (see Section 2.3.3, 'MySQL Installer for Windows').

• On all platforms, the MySQL distribution includes mysql_secure_installation, a command-line utility that automates much of the process of securing a MySQL installation.

• On all platforms, MySQL Workbench is available and offers the ability to manage user accounts (see Chapter 31, MySQL Workbench ).

A password may already be assigned to the initial account under these circumstances:

• On Windows, installations performed using MySQL Installer give you the option of assigning a password.

• Installation using the macOS installer generates an initial random password, which the installer displays to the user in a dialog box.

• Installation using RPM packages generates an initial random password, which is written to the server error log.

• Installations using Debian packages give you the option of assigning a password.

• For data directory initialization performed manually using mysqld --initialize, mysqld Inpaint 8 keygen. generates an initial random password, marks it expired, and writes it to the server error log. See Section 2.10.1, 'Initializing the Data Directory'.

The mysql.user grant table defines the initial MySQL user account and its access privileges. Installation of MySQL creates only a 'root'@'localhost' superuser account that has all privileges and can do anything. If the root account has an empty password, your MySQL installation is unprotected: Anyone can connect to the MySQL server as rootwithout a password and be granted all privileges.

The 'root'@'localhost' account also has a row in the mysql.proxies_priv table that enables granting the PROXY privilege for '@', that is, for all users and all hosts. This enables root to set up proxy users, as well as to delegate to other accounts the authority to set up proxy users. See Section 6.2.18, 'Proxy Users'.

To assign a password for the initial MySQL root account, use the following procedure. Replace root-password in the examples with the password that you want to use.

Start the server if it is not running. For instructions, see Section 2.10.2, 'Starting the Server'.

The initial root account may or may not have a password. Choose whichever of the following procedures applies:

• If the root account exists with an initial random password that has been expired, connect to the server as root using that password, then choose a new password. This is the case if the data directory was initialized using mysqld --initialize, either manually or using an installer that does not give you the option of specifying a password during the install operation. Because the password exists, you must use it to connect to the server. But because the password is expired, you cannot use the account for any purpose other than to choose a new password, until you do choose one.

  1. Ismartphoto 1 7 8. If you do not know the initial random password, look in the server error log.

  2. Connect to the server as root using the password:

  3. Choose a new password to replace the random password:

• If the root account exists but has no password, connect to the server as root using no password, then assign a password. This is the case if you initialized the data directory using mysqld --initialize-insecure.

  1. Connect to the server as root using no password:

  2. Assign a password:

After assigning the root account a password, you must supply that password whenever you connect to the server using the account. For example, to connect to the server using the mysql client, use this command:

To shut down the server with mysqladmin, use this command:

For additional information about setting passwords, see Section 6.2.14, 'Assigning Account Passwords'. If you forget your root password after setting it, see Section B.3.3.2, 'How to Reset the Root Password'.

To set up additional accounts, see Section 6.2.8, 'Adding Accounts, Assigning Privileges, and Dropping Accounts'.

In mathematics, the infinite series1/2 + 1/4 + 1/8 + 1/16 + ··· is an elementary example of a geometric series that converges absolutely. The sum of the series is 1.In summation notation, this may be expressed as

12+14+18+116+⋯=∑n=1∞(12)n=1.{displaystyle {frac {1}{2}}+{frac {1}{4}}+{frac {1}{8}}+{frac {1}{16}}+cdots =sum _{n=1}^{infty }left({frac {1}{2}}right)^{n}=1.}

The series is related to philosophical questions considered in antiquity, particularly to Zeno's paradoxes.

Proof[edit]

As with any infinite series, the sum

12+14+18+116+⋯{displaystyle {frac {1}{2}}+{frac {1}{4}}+{frac {1}{8}}+{frac {1}{16}}+cdots }

is defined to mean the limit of the partial sum of the first n terms

sn=12+14+18+116+⋯+12n−1+12n{displaystyle s_{n}={frac {1}{2}}+{frac {1}{4}}+{frac {1}{8}}+{frac {1}{16}}+cdots +{frac {1}{2^{n-1}}}+{frac {1}{2^{n}}}}

as n approaches infinity.By various arguments,^[a] one can show that this finite sum is equal to

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sn=1−12n.{displaystyle s_{n}=1-{frac {1}{2^{n}}}.}

As n approaches infinity, the term 12n{displaystyle {frac {1}{2^{n}}}} approaches 0 and so s_n tends to 1.

History[edit]

Zeno's paradox[edit]

This series was used as a representation of many of Zeno's paradoxes.^[1] For example, in the paradox of Achilles and the Tortoise, the warrior Achilles was to race against a tortoise. The track is 100 meters long. Achilles could run at 10 m/s, while the tortoise only 5. The tortoise, with a 10-meter advantage, Zeno argued, would win. Achilles would have to move 10 meters to catch up to the tortoise, but the tortoise would already have moved another five meters by then. Achilles would then have to move 5 meters, where the tortoise would move 2.5 meters, and so on. Zeno argued that the tortoise would always remain ahead of Achilles.

The Dichotomy paradox also states that to move a certain distance, you have to move half of it, then half of the remaining distance, and so on, therefore having infinitely many time intervals.^[1] This can be easily resolved by noting that each time interval is a term of the infinite geometric series, and will sum to a finite number.

The Eye of Horus[edit]

The parts of the Eye of Horus were once thought to represent the first six summands of the series.^[2]

In a myriad ages it will not be exhausted[edit]

A version of the series appears in the ancient Taoist book Zhuangzi. The miscellaneous chapters 'All Under Heaven' include the following sentence: 'Take a chi long stick and remove half every day, in a myriad ages it will not be exhausted.'^{[citation needed]}

See also[edit]

Notes[edit]

1. ^For example: multiplying s_n by 2 yields 2sn=22+24+28+216+⋯+22n=1+[12+14+18+⋯+12n−1]=1+[sn−12n].{displaystyle 2s_{n}={frac {2}{2}}+{frac {2}{4}}+{frac {2}{8}}+{frac {2}{16}}+cdots +{frac {2}{2^{n}}}=1+left[{frac {1}{2}}+{frac {1}{4}}+{frac {1}{8}}+cdots +{frac {1}{2^{n-1}}}right]=1+left[s_{n}-{frac {1}{2^{n}}}right].} Subtracting s_n from both sides, one concludes sn=1−12n.{displaystyle s_{n}=1-{frac {1}{2^{n}}}.} Other arguments might proceed by mathematical induction, or by adding 12n{displaystyle {frac {1}{2^{n}}}} to both sides of sn=12+14+18+116+⋯+12n−1+12n{displaystyle s_{n}={frac {1}{2}}+{frac {1}{4}}+{frac {1}{8}}+{frac {1}{16}}+cdots +{frac {1}{2^{n-1}}}+{frac {1}{2^{n}}}} and manipulating to show that the right side of the result is equal to 1.^{[citation needed]}

References[edit]

1. ^ ^abField, Paul and Weisstein, Eric W. 'Zeno's Paradoxes.' From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ZenosParadoxes.html
2. ^Stewart, Ian (2009). Professor Stewart's Hoard of Mathematical Treasures. Profile Books. pp. 76–80. ISBN978 1 84668 292 6.

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