Binomial Theorem And Its Simple Applications Question 150
Question: If $ C_0,C_1,,C_2{{,}^{.}}…….,C_{15} $ are binomial coefficients in $ {{(1+x)}^{15}} $ , then $ \frac{C_1}{C_0}+2\frac{C_2}{C_1}+3\frac{C_3}{C_2}+….+15\frac{C_{15}}{C_{14}}= $
Options:
A) 60
B) 120
C) 64
D) 124
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] General term of the given series is $ r\frac{^{n}C_{r}}{^{n}{C_{r-1}}}=n+1-r $ By taking summation over n, we get $ \sum\limits_1^{15}{r\frac{^{n}C_{r}}{^{n}{C_{r-1}}}=\sum\limits_{n=1}^{15}{(n+1-r)=\sum\limits_1^{15}{(16-r)}}} $
$ =16\times 15-\frac{1}{2}\cdot 15\times 16 $ By using sum of n natural numbers $ =\frac{n(n+1)}{2} $
$ =240-120=120 $
BETA
