Approximating an area by rectangles

[bluemoon2188]

Hi,

I have this problem,

1) Find 1 + 2 + · · · + n by summing the identity (m + 1)² − m² = 2m + 1 from m = 1 to n.
2) Similarly find 1² + 2² + · · · + n² using the identity (m + 1)³ − m³ = 3m² + 3m + 1

Thanks in advance.
bluemoon2188

 

[Yuqing]

Consider the summing the identities provided from 1 through to n. You should be able to obtain a recursive formula for each power in terms of the sums of the lower powers.

 

[bluemoon2188]

oh cool thanks.

bluemoon2188