Question Number 2983 by Syaka last updated on 02/Dec/15

∫_2 ^m f(x) dx = lim_(n → ∞) Σ_(k = 1) ^n (1 +(k/n))(((2k)/n)) m + f(m) = ?

Commented byprakash jain last updated on 03/Dec/15

Σ_(k=1) ^n (((2k)/n)+((2k^2 )/n^2 ))=(2/n)Σ_(k=1) ^n k+(2/n^2 )Σ_(k=1) ^n k^2 = (2/n)∙((n(n+1))/2)+(2/n^2 )∙((n(n+1)(2n+1))/6) ∫_0 ^m f(x)dx=lim_(n→∞) [(n+1)+((2n)/3)+1+(1/n)]