Home
Class 12
MATHS
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

7510

B

7820

C

7830

D

7520

Text Solution

Verified by Experts

The correct Answer is:
B
General term of the given series is
`T_(r) = (3r (1^(2) + 2^(2) + ...+ r^(2)))/(2r +1) = (3r [r ( r +1) (2r +1)])/(6(2r +1))`
`= (1)/(2) (r^(3) + r^(2))`
Now, required sum `= underset(r =1)overset(15)sum T_(r) = (1)/(2) underset(r=1)overset(15)sum (r^(3) + r^(2))`
`= (1)/(2) {[(n (n +1))/(2)]^(2) + (n(n+1) (2n+1))/(6)}_(n=15)`
`= (1)/(2) {(n(n+1))/(2)[(n^(2) +n)/(2) + (2n +1)/(3)]}_(n =15)`
`= (1)/(2) {(n(n+1))/(2) ((3n^(2) + 7n +2))/(6)}_(n=15)`
`= (1)/(2) xx (15 xx 16)/(2) xx ((3 xx 225 + 105 + 2))/(6) = 7820`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the sum of the firt 40 terms of the series 1^(2) -2^(2) + 3^(2) - 4^(2) +……….

Find the sum to n terms of each of the series in 1^2 + (1^2 + 2^2) + (1^2 + 2^2 + 3^2) + ...

Find the sum to n terms of the series 3//(1^2xx2^2)+5//(2^2xx3^2)+7//(3^2xx4^2)+dot

The sum of the first 9 terms of the series 1^3/1 + (1^3 + 2^3)/(1+3) + (1^3 + 2^3 +3^3)/(1 + 3 +5) ..... is :

Find the sum to n terms of the series: 1/(1+1^2+1^4)+1/(1+2^2+2^4)+1/(1+3^2+3^4)+

The sum to 50 terms of the series 3/1^2+5/(1^2+2^2)+7/(1^+2^2+3^2)+….+… is

Find the sum to n terms of the series 1^2+2^2+3^2-4^2+5^2-6^2+. . . .

The 15th term of the series 2 1/2+1 7/(13)+1 1/9+(20)/(23)+.. is

Sum of the first n terms of the series 1/2+3/4+7/8+(15)/(16)+ is equal to