This is a twisted version of a simple thing. I bumped up to this while trying to come up with the formula for summation of squares of natural numbers and if they could be derived as a factor of sum of natural numbers. But, I went down and down into the whirlpool. Finally with some online help, I could find my way out. Do post your comments about whatever you could come up with.
Do you think the approach is wrong? Why?
1 comment:
hey! the way I see it, the mistake is in the indexing.
\sum_{n=1}{N}n^2 = \sum_{n=1}{N}n(n-i) + i\sum_{i=1}{N}n
in which 1\leq i \leq N.
And what you have written seems to suggest that you want to vary i as well. You cannot make i = n-1 when n itself is varying. i has to be a fixed number. Methinks that is the flaw.
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