(b) Compute the sum

\ [ (a + ( 2n+1 ) d ) ^2- (a + (2n ) d ) ^2 + ( a + (2n-1 ) d ) ^2 - (a+ ( 2n-2 ) d ) ^2 + \cdots + (a+d ) ^2 - a^2.\]

Please explain the solution to the problem, thank you.

LWind Dec 6, 2019

#1**+2 **

\ [ (a + ( 2n+1 ) d ) ^2- (a + (2n ) d ) ^2 + ( a + (2n-1 ) d ) ^2 - (a+ ( 2n-2 ) d ) ^2 + \cdots + (a+d ) ^2 - a^2.\]

\(\ [ (a + ( 2n+1 ) d ) ^2- (a + (2n ) d ) ^2 + ( a + (2n-1 ) d ) ^2 - (a+ ( 2n-2 ) d ) ^2 + \cdots + (a+d ) ^2 - a^2] \)

I have not finished this question but i have made a reasonable start.

I expanded each of these squared terms.

The a^2 terms all cancel out.

So you are left with 2 series.

One of those series looks easy to deal with, the other looks a lot more tricky.

Have you tried this and made a good start for yourself ?

Melody Dec 6, 2019