SOLUTION: Sum the Series: 1×2+2×3+3×4+4×5+...+2013×2014 I hope the multiply symbol turned out right! Thank you!

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Question 888240: Sum the Series:
1×2+2×3+3×4+4×5+...+2013×2014
I hope the multiply symbol turned out right! Thank you!
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Sum the Series:
1×2+2×3+3×4+4×5+...+2013×2014

We will use the formulas: sum%28%28k%29%2Ck=1%2Cn%29=n%28n%2B1%29%2F2 and sum%28%28k%5E2%29%2Ck=1%2Cn%29=n%28n%2B1%29%282n%2B1%29%2F6

1×2+2×3+3×4+4×5+...+2013×2014 = sum%28%28k%29%28k%2B1%29%2Ck=1%2C2013%29 = sum%28%28k%5E2%2Bk%29%2Ck=1%2C2013%29 = sum%28%28k%5E2%29%2Ck=1%2C2013%29%2Bsum%28%28k%29%2Ck=1%2C2013%29 =

       2013%282013%2B1%29%282%2A2013%2B1%29%2F6%2B2013%282013%2B1%29%2F2 = 2723058910

Edwin