SOLUTION: Find a nice simple formula for finding what sum is for ANY value n. Explain why it works. 2+4+6+8+...+2n=?

Question 601352: Find a nice simple formula for finding what sum is for ANY value n. Explain why it works.
2+4+6+8+...+2n=?

Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
2+4+6+...+2n = n(n+1). You can prove it by induction. Or you can use the "Gauss-style" method of adding that expression to itself, i.e.

S = 2 + 4 + 6 +...+ 2n
S = 2n+ ... + 2
----------------------
2S = (2n+2) + (2n+2) + ... + (2n+2) = (2n+2)(n)

S = n(n+1)
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