Question

If $a_1$ is the greatest value of $f\left(x\right)=\frac{1}{2+\left[sinx\right]}$ and $a_{n+1}=\frac{(-1{)}^{n+2}}{n+1}+a_n$
Then $\underset{n\to \infty }{lim}{a}_n=$ _________

• A. e
• B. 1
• C.

Answer 1

The correct option is C

$a_1=1,a_2=1-\frac{1}{2},a_3=1-\frac{1}{2}+\frac{1}{3}\dots \dots a_n=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\dots \dots +(-1{)}^{n-1}.\frac{1}{n}\underset{n\to \infty }{lim}{a}_n=lo{g}_{e}2$