# Is there a simplified equation for doing something like this:

Is there a simplified equation for doing something like this:

$$(1x) + (2x) + (3x) + (4x) + (5x)$$

but the number it goes to (the example goes to 5 ) can be variable?

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## 1 Answer

Yes, it's $$\sum_{k=1}^n kx = x\sum_{k=1}^n k = {nx(n+1)\over 2}.$$

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Sorry, my maths skills aren't brilliant (got a C in A levels). Could you explain this a little bit more please? –  AlexMorley-Finch Feb 16 '12 at 15:06
$(1x) + (2x) + \cdots + (nx) = (1 + 2 + \cdots + n)x$, and the sum $1+2+\cdots+n$ is equal to $n(n+1)/2$ –  Chris Taylor Feb 16 '12 at 15:09
Much more sense to me... Thankyou :) –  AlexMorley-Finch Feb 16 '12 at 15:13