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value of 1+(1^(3)+2^(3))/(1+2)+(1^(3)+2^...

value of `1+(1^(3)+2^(3))/(1+2)+(1^(3)+2^(3)+3^(3))/(1+2+3)+……+(1^(3)+2^(3)+….15^(3))/(1+2+…+15)-(1)/(2)(1+2+….+15)` is

A

660

B

620

C

1860

D

1240

Text Solution

Verified by Experts

The correct Answer is:
B
`s = underset(n=1)overset(15)sum (((n(n+1))/(2))^(2))/((n(n+1))/(2)) - (1)/(2) underset(n=1)overset(15)sum n`
`=underset(n=1)overset(15)sum (n (n +1))/(2)- (1)/(2) underset(n=1)overset(15)sumn = (1)/(2) underset(n=1)overset(15)sum n^(2) + (1)/(2) cancel(underset(n=1)overset(15)sum) n - (1)/(2) cancel(underset(n=1)overset(15)sum) n = (1)/(2) xx (15 xx 16 xx 31)/(6) = 620`
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