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

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bluemoon2188	Approximating an area by rectangles 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.