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Write the first five terms of the following sequence and obtai

Question

Write the first five terms of the following sequence and obtain the corresponding series;
$a_{1} = - 1, a_{n} = \frac{a _{n - 1}}{n}, n \geq 2$

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Write the first five terms of the following sequence and obtain the corresponding series;

a_{1} = - 1, a_{n} = \frac{a _{n - 1}}{n}, n \geq 2

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Text solutionVerified

a_{1} = - 1, a_{n} = \frac{a _{n - 1}}{n}, n \geq 2

a_{2} = \frac{a _{1}}{2} = \frac{- 1}{2} a_{3} = \frac{a _{2}}{3} = \frac{- 1}{6} a_{4} = \frac{a _{3}}{4} = \frac{- 1}{24}

a_{5} = \frac{a _{4}}{5} = \frac{- 1}{120}

Hence the first five terms of the sequence are

- 1, \frac{1}{2}, \frac{1}{6}, \frac{1}{24}

and

\frac{1}{120}

The corresponding series is

(- 1) + (\frac{- 1}{2}) + (\frac{- 1}{6}) + (\frac{- 1}{24}) + (\frac{- 1}{120}) + \dots

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Question Text	Write the first five terms of the following sequence and obtain the corresponding series; $a_{1} = - 1, a_{n} = \frac{a _{n - 1}}{n}, n \geq 2$
Answer Type	Text solution:1
Upvotes	150