definite integration

the qn is ondefinite integral as the limit ofa sum/ integration using 1st principle

lim n->âˆž{1/n + n²/(n+1)³ +n²/(n+2)³+.............+1/8n ny1 relpy as fast as possible

1 Answers

1357

Manish Shankar ·2008-11-03 22:42:50

(r from 0 to n) Î£n²/(n+r)³= (1/n) Î£n³/(n+r)³

or (1/n) Î£1/(1+r/n)³

as nâ†’âˆž it can be written in definite integral form as

₀âˆ«¹dx/(1+x)³=[-1/2(1+x)²]₀¹=(-1/2)[1/4-1]=3/8

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