# Geometric Sequence

What does the parentheses mean in this problem?

$$\sum_{K=0}^4 {4\choose K} x^k y^{4-k}$$

4
Sigma Symbol              (4)
(K) x^k y^4-k
K=0


The 4 and the k are in the same parentheses but the 4 is right above the k.It's on top, not side by side.

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You should try to use some markup to draw this as it appears, or even post an image. What you've posted sounds like a poor transcription of a summation series, not a logarithm. –  Sparr Sep 7 '12 at 2:20
I tried to guess what you meant. Does it look right? –  MJD Sep 7 '12 at 4:47
@MJD no idea if you got it right, but if we assume that some newlines were lost after the 4 and before the K=0 then you did a remarkable job of reassembling it! –  Sparr Sep 8 '12 at 2:34
@Sparr Thanks, but I think OP deserves credit for making such a thorough effort to explaining what they meant. –  MJD Sep 8 '12 at 2:36
thanks MJD for making my OP clearer. –  CrewdNBasic Sep 15 '12 at 20:53

The symbol ${4\choose k}$ means "number of ways to choose $k$ objects out of $4$ objects," without taking order into account. You can read more here.

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Thamks a lot! sorry for the mis label –  CrewdNBasic Sep 15 '12 at 20:52

If you mean $\displaystyle\binom{4}{k}$ then this is a binomial coefficient, generally defined as $\displaystyle\binom{n}{k}=\frac{n!}{k!(n-k)!}$

$($for $0\leq k\leq n$, and where $n!=n\cdot (n-1)\cdot (n-2)\cdots \;3\cdot 2\cdot 1)$

Not quite sure what your question has to do with logarithms though...

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thanks a lot! sorry for the mis label –  CrewdNBasic Sep 15 '12 at 20:52