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I am working in analyzing an algorithm in recurrence, but I end up in the following sequence:


I tried to make an equivalent summation but I failed. Is there a technique on making summations?

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It’s not clear just what sum you’re taking. Are you summing the displayed expression over some range of values of $n$? – Brian M. Scott Feb 11 '13 at 3:35
@BrianM.Scott I mean how can I represent this sequence in the sigma (Σ) notation. – MIH1406 Feb 11 '13 at 3:43
Just these four terms? I wouldn’t bother, though you could combine the first three and make it $$n^2+5n^2\sum_{k=1}^3\frac1{2^{2k}}\;.$$ – Brian M. Scott Feb 11 '13 at 3:44
MIH, the word "sequence" doesn't mean what you think it means. Sequences have commas; summations have plus signs. – Gerry Myerson Feb 11 '13 at 3:50

$$ \sum_{k=1}^N (\frac {5 n^2} {2^{2k}} +\frac {n^2} N) $$

Without knowing more about the algorithm you are analyzing, it is kind of difficult to provide the correct summation.

The above sum will give the expression in your question with N=3.

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