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Let a 1 1 and for n geq 1 a n 1 frac12 a n fracn 2 2 n 1n 2: null (Mathematics) | DivineJEE

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Mathematics

Exam 2026 21st January Shift 1

Mathematics

Let

\mathrm{a}_{1}=1

and for

\mathrm{n} \geq 1, \mathrm{a}_{\mathrm{n}+1}

\\

=\frac{1}{2} a_{n}+\frac{n^{2}-2 n-1}{n^{2}(n+1)^{2}}

. Then

\left|\sum_{n=1}^{\infty}\left(a_{n}-\frac{2}{n^{2}}\right)\right|

is equal to

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