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What's a way to sum over the first n items in a sequence, for example the sequence defined by $2^{k-1}\cdot k$ for $k\in\mathbb{Z},k>0$?

I do these by hand all the time but am a bit tired of doing this, so I'm looking for a way in mathematica.

Sorry if someone already asked this before, couldn't find any similar questions.

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closed as off-topic by ssch, Sjoerd C. de Vries, Artes, Mr.Wizard Dec 4 '13 at 18:30

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question arises due to a simple mistake such as a trivial syntax error, incorrect capitalization, spelling mistake, or other typographical error and is unlikely to help any future visitors, or else it is easily found in the documentation." – ssch, Sjoerd C. de Vries, Artes, Mr.Wizard
If this question can be reworded to fit the rules in the help center, please edit the question.

2 Answers 2

up vote 3 down vote accepted

Use Sum

Sum[2^(k - 1) k, {k, 1, n}]

If you hit F1 to open up help center and search for sum, it will be the first result.

An Overview of the Mathematica Help System

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Brilliant, thanks, I'll accept in 10 minutes. –  simonzack Dec 4 '13 at 16:28

Same as ssch's but with fancy typesetting - using EscsumtEsc, and Ctrl+^ for the power term:-

\*UnderoverscriptBox[\(\[Sum]\), \(k = 1\), \(n\)]\(
\*SuperscriptBox[\(2\), \(k - 1\)] k\)\)
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