The first term of an A.P. of consecutive inte | vedclass

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Question

(d) ${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)({

Vedclass · Accepted Answer

${p^3} + {(p + 1)^3}$

Vedclass · Answer

(d) ${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}$.

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

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