Sequence And Series Question 510
Question: The first term of an A.P. of consecutive integers is $ p^{2}+1 $ The sum of $ (2p+1) $ terms of this series can be expressed as
Options:
A) $ {{(p+1)}^{2}} $
B) $ {{(p+1)}^{3}} $
C) $ (2p+1){{(p+1)}^{2}} $
D) $ p^{3}+{{(p+1)}^{3}} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ {S_{2p+1}}=\frac{2p+1}{2}{2(p^{2}+1)+(2p+1-1),1} $ $ =( \frac{2p+1}{2} ),(2p^{2}+2p+2)=(2p+1)(p^{2}+p+1) $ $ =p^{3}+{{(p+1)}^{3}} $ .
BETA
