If α,β are the roots of the equation, x2−x−1=0 and Sn=2023αn+2024βn, then
Held on 27 Jan 2024 · Verified 6 Jul 2026.
2S12=S11+S10
S12=S11+S10
2S11=S12+S10
S11=S10+S12
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Let $a_{1}=1$ and for $n \geqslant 1, a_{n+1}=\frac{1}{2} a_{n}+\frac{n^{2}-2 n-1}{n^{2}(n+1)^{2}}$. Then $\left|\sum_{n=1}^{\infty}\left(a_{n}-\frac{2}{n^{2}}\right)\right|$ is equal to $\_\_\_\_$.
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