Let C r denote the coefficient of x^(r) in the binomial expansion of (1+x)ⁿ, n, 0≤ r≤ n. If P n =C₀-C₁+(2²)/3C₂-(2³)/4C₃+ +((-2)ⁿ)/(n+1)C n, then the value of Σ n=1 ²⁵1/(P 2n) equals.

Binomial Theorem and Its Simple Applications: JEE Main 2026 Mathematics question

JEE Main 2026 · 22 Jan, Evening shift · Q16

JEE Main 202622 Jan, Evening shiftMathematicsMediumBinomial Theorem and Its Simple Applications131× since 2002

Let

C_r

denote the coefficient of

x^r

in the binomial expansion of

(1+x)^n

n\in\mathbb{N}

0\le r\le n

. If

P_n=C_0-C_1+\frac{2^2}{3}C_2-\frac{2^3}{4}C_3+\dots+\frac{(-2)^n}{n+1}C_n

, then the value of

\sum_{n=1}^{25}\frac{1}{P_{2n}}

equals.