Why doesn't the integration of the general term of an A.P. give its sum? Integration sums up finctions, so if I integrate the general term function of an A.P., I should get its sum.(adsbygoogle = window.adsbygoogle || []).push({});

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2,4,6,8,.....

T=2+(n-1)2=2n

[itex]\int T dn[/itex]=n^2 ..(1)

Sum=S=(n/2)(4+(n-1)2)=(n/2)(2+2n)=n+(n^2) ..(2)

Why aren't these two equal?

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# Summing up an Arithmetic Progression via Integration?

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