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If 1^2 + 2^2 + 3^2...100^2 = A and 1^3 + 2^3 + 3^3...100^3 = B then 1^2*2 + 2^2*3 + 3^2*4 + 4^2*5...100^2*101 = ??

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If
1^2 + 2^2 + 3^2 + ................. 100^2 = A &
1^3 + 2^3 + 3^3 + .................. 100^3 = B
Then
1^2*2 + 2^2*3 + 3^2*4 + 4^2*5 ........ 99^2*100 + 100^2*101=??

posted Aug 5, 2015 by anonymous

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1 Solution

+4 votes
 
Best answer

1^2*2 + 2^2*3 + 3^2*4 + 4^2*5 ........ 99^2*100 + 100^2*101
= 1^2(1+1) + 2^2(2+1) + 3^2(3+1) + ........... + 100^2(100+1)
= 1^3 + 1^2 + 2^3 + 2^2 + 3^3 + 3^2 + ......... + 100^3 + 100^2
= (1^3 + 2^3 + 3^3)+(1^2 + 2^2 + 3^2 + ....... + 100^2)
= A + B

solution Jan 3, 2016 by Jaspalsingh Parmar
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