Limit[(Sum[i^0.5, {i, n}] - n^0.5)/n^1.5, n -> \[Infinity]]
F[x] = [ 1^0.5 + 2^0.5 ....... (n-1)^0.5 ] / n*n^0.5
Find Limit f(x) where n tends to infinity.
Thanks
No, the sum is not equal to the integral.
Try this: Draw x and y coordinate axes. Sketch rectangles of height for n = 1, 2, 3, 4, 5 (say), where the base of each rectangle is the line segment from (n, 0) to (n+1, 0). Now sketch the curves and . is the total area of the first n rectangles. Can you "see" the inequality now?