Tuesday, 18 February 2014

calculus - Solving the Riemann Sum sumni=1(1+frac6in)3(frac2n)?



So I have the Riemann sum. ni=1(1+6in)3(2n). From my understanding that turns into (2n)ni=1(1+6in)3 and what is really perplexing me is that that summation turns into
(2n)ni=1(1+6in)3(2n4)ni=1(n+6i)3From there on out I can solve the summation, but I'm having trouble understanding how the n was pulled out and the new summation was formed. If someone could explain that bit I would greatly appreciate it, thanks in advance!


Answer



2nni=1(1+6in)3=n3n32nni=1(1+6in)3=2nn3ni=1n3(1+6in)3

and n3(1+6in)3=(n+6inn)3=(n+6i)3


No comments:

Post a Comment

real analysis - How to find limhrightarrow0fracsin(ha)h

How to find lim without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...