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MATHEMATICS · Single correct · CBSE · Mathematics · Binomial Theorem · Binomial Theorem
Problem Which of the following identities holds for all integers n ≥ 1 n \ge 1 n ≥ 1 1 ≤ r ≤ n 1 \le r \le n 1 ≤ r ≤ n n C r + n C r − 1 = n + 1 C r + 1 {}^{n}C_{r}+{}^{n}C_{r-1} = {}^{n+1}C_{r+1} n C r + n C r − 1 = n + 1 C r + 1 n C r + n C r − 1 = n + 1 C r {}^{n}C_{r}+{}^{n}C_{r-1} = {}^{n+1}C_{r} n C r + n C r − 1 = n + 1 C r n C r + n C r − 1 = n C r + 1 {}^{n}C_{r}+{}^{n}C_{r-1} = {}^{n}C_{r+1} n C r + n C r − 1 = n C r + 1 n C r + n C r − 1 = n + 1 C r − 1 {}^{n}C_{r}+{}^{n}C_{r-1} = {}^{n+1}C_{r-1} n C r + n C r − 1 = n + 1 C r − 1 Browse the problem library