Let a1=1, an+1=an(fracsqrtn+sin nn) and bn=an^2 for all ninN. Then which of the following statements is/are correct?

Q31Section B (Section B)31 of 60

Convergence of a recursively defined series

Let $a_1=1$ , $a_{n+1}=a_n\bigl(\frac{\sqrt{n}+\sin n}{n}\bigr)$ and $b_n=a_n^2$ for all $n\in\mathbb{N}$ . Then which of the following statements is/are correct?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

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