Sequence And Series Question 144
Question: Sum of the $ n $ terms of the series $ \frac{3}{1^{2}}+\frac{5}{1^{2}+2^{2}}+\frac{7}{1^{2}+2^{2}+3^{2}},+…is $
[Pb. CET 1999; RPET 2001]
Options:
A) $ \frac{2n}{n+1} $
B) $ \frac{4n}{n+1} $
C) $ \frac{6n}{n+1} $
D) $ \frac{9n}{n+1} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ T_{n}=\frac{(2n+1)}{n(n+1)(2n+1)/6}=\frac{6}{n(n+1)} $ $ S_{n}=\Sigma (T_{n})=\Sigma ,6,[ \frac{1}{n}-\frac{1}{n+1} ] $ $ =6[ 1-\frac{1}{n+1} ] $ $ S_{n}=\frac{6n}{n+1} $ .
BETA
