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'Telescoping Series' printed from http://nrich.maths.org/
Why do this problem?
The problem gives step by step guidance so that learners only need
to apply what they know about the Binomial expansion of $(k+1)^n$
and do some simple algebraic manipulation to be able to find
general formulae for the sums of powers of the integers. As the
name suggests the method makes use of the 'telescoping' property so
that all the intermediate terms disappear leaving only the first
You might choose to introduce this method just for the sum of
the squares of the integers as pictured in the pyramid
What is $[2^2-1^2] + [3^2-2^2] +
[4^2-3^2] + \cdots + [(n + 1)^2-n^2]$?
Try the problems
More Sequences and Series,
OK Now Prove It