Write the first five terms of the following s | vedclass

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Question

$a_{1}=-1, a_{n}=\frac{a_{n-1}}{n}, n\, \geq \,2$

$\Rightarrow a_{2}=\frac{a_{1}}{2}=\frac{-1}{2}$

$a_{3}=\frac{a_{2}}{3}=\frac{-1}{6}$

$a_{4

Vedclass · Accepted Answer

$(-1)+\left(\frac{-1}{2}\right)+\left(\frac{-1}{6}\right)+\left(\frac{-1}{24}\right)+\left(\frac{-1}{120}\right)+\ldots$

Vedclass · Answer

$a_{1}=-1, a_{n}=\frac{a_{n-1}}{n}, n\, \geq \,2$

$\Rightarrow a_{2}=\frac{a_{1}}{2}=\frac{-1}{2}$

$a_{3}=\frac{a_{2}}{3}=\frac{-1}{6}$

$a_{4}=\frac{a_{3}}{4}=\frac{-1}{24}$

$a_{5}=\frac{a_{4}}{5}=\frac{-1}{120}$

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 $(-1)+\left(\frac{-1}{2}\right)+\left(\frac{-1}{6}\right)+\left(\frac{-1}{24}\right)+\left(\frac{-1}{120}\right)+\ldots$

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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