How to calculate certain sum? [with detailed answer]

math

#1

alt text


#2

It is a simple exercise on sum of the geometric progression.
We have by the formula
(a + b)^2 = a^2 + 2 * a * b + b^2
that
Sum[(2^k + 1/2^k)^2 : 1<=k<=n] =
Sum[2^(2 * k) + 2 + 1/(2^(2 * k)) : 1<=k<=n] =
2 * n + Sum[4^k + (1/4)^k : 1<=k<=n] =
2 * n + (4^n-1) * 4/3 - ((1/4)^n-1) * 1/3 =
1/3 * (-3 - 4^(-n) + 4^(1 + n) + 6 * n)

Also refer to this


#3

I don’t quite understand your question. Are you asking how to translate the above expression to code ? Please clarify


#4

no this is math problem,i want to know what is it


#5

@lashabuxo
No way you can delete this now after I write the explanation :stuck_out_tongue:
If it is your homework and you don’t want others to see that you ask for help then it will be a lesson to you.