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Category: Algebra

Given-only-the-standard-result-r-1-N-r-2-1-6-N-N-1-2N-1-is-applied-to-determining-the-series-1-2-2-2-2-3-2-2-4-2-5-2-2-6-2-7-2-2-n-1-2-n-2-where-n-is-odd-show-that-it-is-given

Question Number 669 by 112358 last updated on 21/Feb/15 GivenonlythestandardresultNr=1r2=16N(N+1)(2N+1)isappliedtodeterminingtheseries$$\mathrm{1}^{\mathrm{2}} +\mathrm{2}×\mathrm{2}^{\mathrm{2}} +\mathrm{3}^{\mathrm{2}} +\mathrm{2}×\mathrm{4}^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} +\mathrm{2}×\mathrm{6}^{\mathrm{2}} +\mathrm{7}^{\mathrm{2}} +…+\mathrm{2}\left({n}−\mathrm{1}\right)^{\mathrm{2}} +{n}^{\mathrm{2}}…