If , is equal…

MATHEMATICS · Single correct · CBSE · Mathematics · Binomial Theorem · Binomial Theorem

Problem

If (1+x)n=∑r=0nnCrxr(1+x)^n = \sum_{r=0}^{n} {}^n C_r x^r , (1+C1C0)(1+C2C1)…(1+CnCn−1)\left(1 + \frac{C_1}{C_0}\right) \left(1 + \frac{C_2}{C_1}\right) \dots \left(1 + \frac{C_n}{C_{n-1}}\right) is equal to (1) nn−1(n−1)!\frac{n^{n-1}}{(n-1)!} (2) (n+1)n−1(n−1)!\frac{(n+1)^{n-1}}{(n-1)!} (3) (n+1)nn!\frac{(n+1)^n}{n!} (4) (n+1)n+1n!\frac{(n+1)^{n+1}}{n!}

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