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# How to calculate certain sum? [with detailed answer]

 0 asked 17 Jan '13, 19:10 73●1●5●8 accept rate: 0% 6.7k●62●119●138 I don't quite understand your question. Are you asking how to translate the above expression to code ? Please clarify (17 Jan '13, 19:18) junior944★ no this is math problem,i want to know what is it (17 Jan '13, 19:25) @lashabuxo No way you can delete this now after I write the explanation :P 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. (17 Jan '13, 21:15)

 1 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 http://www.wolframalpha.com/input/?i=Sum[%282^k+%2B+1%2F2^k%29^2%2C+{k%2C+1%2C+n}] answered 17 Jan '13, 19:34 6.7k●62●119●138 accept rate: 12%
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question asked: 17 Jan '13, 19:10

question was seen: 764 times

last updated: 17 Jan '13, 21:15