JEE MainMathematicsModerateTheory of Equations

The first term of an A.P. of consecutive integer is p^2 + 1.
The sum of (2p + 1) terms of this series can be expressed as

Show answer and solution

S_{n} = \frac{n}{2}\ \lbrack 2a + (n - 1)d\rbrack

n = 2p +1
a = p^2 + 1
d = 1

\Rightarrow S_{n} = \frac{(2p + 1)}{2}\left\lbrack 2p^{2} + 2 + 2p \right\rbrack

= 2p^{3} + 3p^{2} + 3p + 1

= \ p^{3} + (p + 1)^{3}

Source: Grass-G / M-06 Mathematics Paper 14 October.docx

Need a video for this idea?

Scan any doubt from your notes and get a whiteboard explanation.