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Find sun of first 15 term of series 1+6...

Find sun of first 15 term of series `1+6+(9(1^2+2^2+3^2))/(7)+(12(1^2+2^2+3^2+4^2))/(9)+`?. (a) `7620` (b) `7280` (c) `7820` (d) `7067`

A

7820

B

7830

C

7520

D

7510

Text Solution

Verified by Experts

The correct Answer is:
A
`sum_(r=1)^(15)(3r)/(2r+1)(sum_(k=1)^(r)K^(2))`
`=sum_(r=1)^(15)(3r)/((2r+1))(r(r+1)(2r+1))/(6)=(1)/(2)sum_(r=1)^(15)(r^(3)+r^(2))=(1)/(2)sum_(r=1)^(15)(r^(3))+(1)/(2)sum_(r=1)^(15)r^(2)=(1)/(2)((15.16)/(2))^(2)+(1)/(2)((15.16.31)/(6))`
`=(1)/(2)(15.8)^(2)+(1)/(2)(5.8.31)=7820`
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