If 1 1 3 + 1 2 4 + 1 3 5 + + 1 n(n+2) = n(3 n+p) 2(n+1)(n+2) then is equal to

Mathematics · JEE Main · NTA Exams — Progression and Series

If \(\frac{1}{1 \times 3}+\frac{1}{2 \times 4}+\frac{1}{3 \times 5}+\ldots+\frac{1}{n(n+2)}=\frac{n(3 n+p)}{2(n+1)(n+2)}\)
then is equal to

1. \(1-\mathrm{i} \sqrt{3}\)
2. \(-1+i \sqrt{3}\)
3. \(4 \sqrt{3} \mathrm{i}\)
4. \(-\mathrm{i} \sqrt{3}\)

Answer

(C) 4 3 i

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