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Derivation of the Sum of a Series
Posted:
Sep 23, 2001 6:43 PM
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Hello All,
I need to derive the following.
The sum from i=1 to i=n of i^2. The result of the derivation should be
[n(n+1)(2n+1)]/6.
A similar derivation for the sum from i=1 to i=n of i is the following
Let X= sum from i=1 to i=n of i
1 + n =n+1
2 + n-1 =n+1
3 + n-2 =n+1 n terms
. + . =n+1
. + . =n+1
n + 1 =n+1
X + X =n(n+1)
Therefore, X=[n(n+1)]/2
Similarly, a derivation for the sum from i=1 to i=n of i^3 would be
great.
If anyone knows how to do this, please EMail me at ea342@stern.nyu.edu
Thank You So Much,
Eric
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