Mathematics: For every positive integer n, the nth term of a sequence is given by a_{n} = rac{1}{n} - rac{1}{n + 1}. what is the sum of the first 100 terms of this sequence?

Step-by-step explanation:we know that items on a test represent the of the itemssoby proportionFind how many items were on the test...

For every positive integer n, the nth term of - id1799781, tylervreeland022202

Ответ:

hjgdk6018

31.12.2021

Mathematics

The sum telescopes nicely:

$\displaystyle\sum_{n=1}^{100}a_n=\left(\frac11-\frac12\right)+\left(\frac12-\frac13\right)+\left(\frac13-\frac14\right)+\cdots+\left(\frac1{99}-\frac1{100}\right)+\left(\frac1{100}-\frac1{101}\right)$

$\implies\displaystyle\sum_{n=1}^{100}a_n=1-\frac1{101}=\boxed{\frac{100}{101}}$

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Ответ:

milkshakegrande101

17.07.2022

Mathematics

$50\ items$

Step-by-step explanation:

we know that

items on a test represent the $6\%$ of the items

by proportion

Find how many items were on the test

$\frac{3}{6}\frac{items}{\%} =\frac{x}{100}\frac{items}{\%} \\ \\x=100*3/6\\ \\x=50\ items$

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For every positive integer n, the nth term of a sequence is given by a_{n} = \frac{1}{n} - \frac{1}{n + 1}. what is the sum of the first 100 terms of this sequence?

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