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MCQMediumJEE Main 2026 · 22 January, Shift 2Simple Applications

Mathematics Question from JEE Main 2026 · 22 January, Shift 2

Let CrC_r denote the coefficient of xrx^r in the binomial expansion of (1+x)n(1+x)^n, n∈Nn\in\mathbb{N}, 0≤r≤n0\le r\le n. If

Pn=C0−C1+223C2−234C3+⋯+(−2)nn+1Cn,P_n = C_0 - C_1 + \frac{2^2}{3}C_2 - \frac{2^3}{4}C_3 + \cdots + \frac{(-2)^n}{n+1}C_n,

then the value of

∑n=1251P2n\sum_{n=1}^{25} \frac{1}{P_{2n}}

equals

  • A

    650650

  • B

    525525

  • C

    675675

  • D

    580580

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