Home
Class 12
MATHS
Sum of first 20 terms of 3/1^2 + 5/(1^2...

Sum of first 20 terms of ` 3/1^2 + 5/(1^2 + 2^2) + 7/(1^2 + 2^2 + 3^2) `+... upto 20 terms is :

Text Solution

Verified by Experts

`T_n=(2n+1)/(n(n+1)(2n+1)`
`=6/(n(n+1)`
`=6(1/n-1/(n+1))`
`T_1=6(1-1/2)`
`T_2=6(1/2-1/3)`
`T_3=6(1/3-1/4)`
`t_20=6(1/20-1/21)`
`T_1+T_2+T_3...T_20=6(1-1/21)`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

The sum up to 60 terms of 3/(1^2) + 5/(1^2 + 2^2) + 7/(1^2 + 2^2 + 3^2) + ……. is equal to

The sum up to 60 terms of 3/(1^2) + 5/(1^2 + 2^2) + 7/(1^2 + 2^2 + 3^2) + ……. is equal to

The sum (3)/(1^(2)) + (5)/(1^(2) + 2^(2)) + (7)/(1^(2)+ 2^(2) + 3^(2)) + ….. upto 11 terms is

the sum 3/1^2+5/(1^2+2^2)+7/(1^2+2^2+3^2)+....... upto 11 terms

1^(2) + 3^(2) + 5^(2) + …. upto n terms =

If the sum (3)/(1^(2)) + (5)/(1^(2) + 2^(2)) + (7)/(1^(2) + 2^(2) + 3^(2)) + …+ upto 20 terms is equal to (k)/(21) , then k is equal to

3/(1^2 2^2)+5/(2^2 3^2)+7/(3^2 4^2)+ . . . upto 10th term

Find the sum of first n terms of the series 3/1^2+5/(1^2+2^2)+7/(1^2+2^2+3^2) +.... .

1,2,3…..sum of 20 term is