Thursday, January 14, 2016

sequences and series - How do I find the sum of sumlimitsik=1nftyfrack2k+1=1?


As shown in the title, how do I find the sum of:


k=1k2k+1=1


Answer



HINT:


Note that for |x|<1, f(x)=k=1xk=x1x implies that


x2f(x)=k=1kxk+1


Then, let x=1/2


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