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The sum (3 xx 1^(3))/(1^(2)) (5 xx (1^...

The sum
`(3 xx 1^(3))/(1^(2)) (5 xx (1^(3) + 2^(3)))/(1^(2) + 2^(2)) + (7 xx (1^(3) + 2^(3) + 3^(3)))/(1^(2) +2^(2) + 3^(2))` upto 10th term is

A

680

B

620

C

660

D

600

Text Solution

Verified by Experts

The correct Answer is:
C
`T_(r)=((2r+1)(1^(3) +2^(3)+…….+r^(3))/(1^(2) +2^(2)+………….+r^(2)))`
`T_(r) =((2r+1)((r(r+1))/2)^(2))/(r(r+1)(2r+1))/6`
`T_(r) = 3/2r(r+1)`
Sum up to 10th term `=3/2sum_(r=1)^(10)r(r+1)=660`
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