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)n∑i=1(1+6in)3→(2n4)n∑i=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
2nn∑i=1(1+6in)3=n3n32nn∑i=1(1+6in)3=2n⋅n3n∑i=1n3(1+6in)3
and n3(1+6in)3=(n+6inn)3=(n+6i)3
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