1+3+5+...+(2n-1)=∑(2k-1)(adsbygoogle = window.adsbygoogle || []).push({});

but (2k-1)=k^{2}-(k-1)^{2}

summing we use the telescoping property and deduce that ∑(2k-1)=n^{2}-0^{2}=n^{2}

This seems accurate to me. Now my question is this a proper use of the telescoping property. In the least it reveals the proper answer, which can then be proved by induction.

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# Telescoping sum

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