Prove by induction that tan⁻¹ 13+tan⁻¹ 17+·s+tan⁻¹ 1 n²+n+1 =tan⁻¹ n n+2.

Answer: Proved. Each term tan⁻¹ 1 n²+n+1 =tan⁻¹(n+1)-tan⁻¹n telescopes; with tan⁻¹(n+1)-tan⁻¹1=tan⁻¹ n n+2. JEE Advanced 1993 · Binomial Theorem — verified solution by the Vidaara Team.

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[JEE Advanced 1993] prove by induction that tan 1 13 tan 1 17 tan 1 1 n

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Prove by induction that $\tan^{-1}\frac13+\tan^{-1}\frac17+\cdots+\tan^{-1}\frac1{n^2+n+1}=\tan^{-1}\frac n{n+2}$.

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VAVidaara Admin ✓ Vidaara Team ✓ Accepted · 2d ago ▲ 0

Answer: Proved.

Each term $\tan^{-1}\frac1{n^2+n+1}=\tan^{-1}(n+1)-\tan^{-1}n$ telescopes; with $\tan^{-1}(n+1)-\tan^{-1}1=\tan^{-1}\frac n{n+2}$.

JEE Advanced 1993 · Binomial Theorem — verified solution by the Vidaara Team.

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