A) \[{{(p+1)}^{2}}\]
B) \[{{(p+1)}^{3}}\]
C) \[(2p+1){{(p+1)}^{2}}\]
D) \[{{p}^{3}}+{{(p+1)}^{3}}\]
Correct Answer: D
Solution :
\[{{S}_{2p+1}}=\frac{2p+1}{2}\{2({{p}^{2}}+1)+(2p+1-1)\,1\}\] \[=\left( \frac{2p+1}{2} \right)\,(2{{p}^{2}}+2p+2)=(2p+1)({{p}^{2}}+p+1)\] \[={{p}^{3}}+{{(p+1)}^{3}}\].You need to login to perform this action.
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