SOLUTION: 1+5+14+30+55........ Find sum to n terms.

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Question 954448: 1+5+14+30+55........
Find sum to n terms.
Answer by hemu_da(13) About Me  (Show Source):
You can put this solution on YOUR website!
It is the series of sum of the first n%5E2 terms..
We know that....
Sum of first n term is n%28n%2B1%29%2F4
Sum of the square of the first n term is %28n%28n%2B1%29%282n%2B1%29%29%2F6

Sum of the cube of the first n numbers is %28n%5E2%28n%2B1%29%5E2%29%2F2
Given that..

1%2B5%2B14%2B30%2B55%2B.........
Or
%28n%28n%2B1%29%282n%2B1%29%29%2F6.
We can write this series also as--- sum= sum%28%28%28n%28n%2B1%29%282n%2B1%29%29%2F6%29%2Cn=1%2Cn%29.
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Sum=sum%28%28%28%28n%5E2%2Bn%29%282n%2B1%29%29%2F6%29%2Cn=1%2Cn%29
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Sum=sum%28%28%282n%5E3%2B3n%5E3%2Bn%29%2F6%29%2Cn=1%2Cn%29
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Sum=sum%28%28%28%28n%5E3%29%2F3%29%2B%28%28n%5E2%29%2F2%29%2B%28n%2F6%29%29%2Cn=1%2Cn%29
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Sum=
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Sum=
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Sum= %28n%28n%2B1%29%28n%28n%2B1%29%2B%282n%2B1%29%2B1%29%29%2F12
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Sum= %28n%28n%2B1%29%28n%5E2%2B3n%2B2%29%29%2F12
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Sum= %28n%28n%2B1%29%28n%2B1%29%28n%2B2%29%29%2F12
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Sum= %28n%28n%2B1%29%5E2%28n%2B2%29%29%2F12.... Ans..
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To varify this formula lets take n=4...
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Sum=%284%284%2B1%29%5E2%284%2B2%29%29%2F12
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Sum=%284%2A25%2A6%29%2F12
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Sum= 50.
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In the series... Sum of first 4 terms= 1+5+14+30 = 50..
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Which is equal to the our calculated Ans....