Given below are two statements. STATEMENT - 1: _ r=n ^ n 1 r+1 ^ n C_ r x ^ r = 1 (n+1) x…
Mathematics · JEE Main · NTA Exams — Binomial Theorem And Its Simple Applications
Given below are two statements.
STATEMENT - 1: \(\sum_{r=n}^{n} \frac{1}{r+1}{ }^{n} C_{r} \mathbf{x}^{r}\) \(=\frac{1}{(n+1) \mathbf{x}}\left\{(1+\mathbf{x})^{n+1}-1\right\}\)
STATEMENT - 2: \(\sum_{r=0}^{n} \frac{{ }^{n} C_{r}}{r+1}=\frac{z^{n+1}}{n+1}\)
In the light of the above statements, choose the correct answer from the options given below:
- Both Statements are true and Statement - 2 is the correct explanation for Statement - 1
- Both Statements are true and Statement - 2 is not the correct explanation for Statement - 1
- Statement - 1 is true and Statement - 2 is false
- Statement - 1 is false and Statement - 2 is true
Answer
(C) Statement - 1 is true and Statement - 2 is false
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