Question

Sum of n terms of series 1.3 + 3.5 + 5.7 + ______ is

पर्याय

• `1/3 n(n + 1)(2n + 1) - n`

• `3/2 n(n + 1)(2n + 1) - n`

• `4/5 n(n + 1)(2n + 1) - n`

• `2/3 n(n + 1)(2n + 1) - n`

Answer 1

`2/3 n(n + 1)(2n + 1) - n`

Explanation:

T_n = [n^th term of 1.3.5 ......] × [n^th term of 3.5.7....]

or T_n = [1 + (n – 1) × 2] × [3 + (n – 1) × 2]

or T_n = (2n – 1)(2n + 1) = (4n² – 1)

S_n = `sum T_n = sum (4n^2 - 1) = 4. sumn^2 - sum1`

= `(4 xx n(n + 1)(2n + 1))/6- n`

= `2/3 n (n + 1)(2n + 1) - n`