Mathematics · 2026
JEE Main · 22 January 2026, Shift 2 · Q9
Let C_r denote the coefficient of x^r in the binomial expansion of (1+x)^n, n ∈ N, 0 ≤ r ≤ n. If P_n=C_0-C_1+2^2/3 C_2-2^3/4 C_3+…..+((-2)^n)/(n+1)…
Let $\displaystyle \mathrm{C}_{\mathrm{r}}$ denote the coefficient of $\displaystyle x^{\mathrm{r}}$ in the binomial expansion of $\displaystyle (1+x)^{\mathrm{n}}, \mathrm{n} \in \mathbf{N}, 0 \leq \mathrm{r} \leq \mathrm{n}$. If $\displaystyle P_n=C_0-C_1+\frac{2^2}{3} C_2-\frac{2^3}{4} C_3+\ldots . .+\frac{(-2)^n}{n+1} C_n$, then the value of $\displaystyle \sum_{n=1}^{25} \frac{1}{P_{2 n}}$ equals.
Official answer
From NTA’s final answer key for this paper.
(2)
$\displaystyle 675$
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JEE Main 2026 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.