Sequence And Series Question 120
Question: The sum of $ n $ terms of the series whose $ n^{hth} $ term is $ n(n+1) $ is equal to
Options:
A) $ \frac{n(n+1)(n+2)}{3} $
B) $ \frac{(n+1)(n+2)(n+3)}{12} $
C) $ n^{2}(n+2) $
D) $ n(n+1)(n+2) $
Show Answer
Answer:
Correct Answer: A
Solution:
$ T_{n}=n^{2}+n $
$ \Rightarrow $ $ S_{n}=\Sigma T_{n}=\Sigma n^{2}+\Sigma n $ $ =\frac{n,(n+1),(2n+1)}{6}+\frac{n,(n+1)}{2} $ $ =\frac{n,(n+1)}{6},{2n+1+3}=\frac{n,(n+1),(n+2)}{3} $ .
BETA
