Question

2 2/3+2 2/15+2 2/35 …+2 2/399

Answer 1

Answer:

I assume the series to be like the following:

Let  S =2* 2/3 + 2* 2/15 + 2 X 2/35 +⋯ + 2 *2/399  

Assuming there are  n  terms:

S = 2n + 2 ⋅[ 1/3 +1/15 + 1/35 +⋯ + 1/399]  

    =2n + 2⋅ [ 1/1×3 + 1/3 × 5 + 1/ 5 ×7 + ⋯ + 1/19 × 21]  

⟹n=10  

∴S = ( 2 × 10 ) +2 ∑ n=1 1/(2n−1)(2n+1)  

=20 + 2∑n=1 1/2 ⋅ ( 1/2n−1 −1/2n+1)

=20 + ∑n=1 (/12n−1  −1/2n+1)  

=20+(1/1−1/3)+(1/3−1/5)+(1/5−1/7)+⋯+(1/19−1/21)

=20+ (1/1 − 1/21)

=20+20/21

=20*20/21

Answer 2

Answer:

Answer is 440/21

since 20+20/21= 440/21