Question

Evaluate :


$\frac{4}{7} - \frac{5}{ {7}^{2} } + \frac{4}{ {7}^{3}} - \frac{5}{ {7}^{4} } + \frac{4}{ {7}^{5} } - \frac{5}{ {7}^{6} } ...to \: infinty$

✔️✔️ quality answer needed✔️✔️​

Answer 1

4[ 1/7 + 1/7^3 +1/7^5+.....] = 4/7[1+1/7^2 +1/7^4 ......] =4/7 [ 1/(1-1/49)] = 4/7 x 49/48 =7/12

-5/49[ 1 + 1/49 + 1/49^2 +....] = -5/49[ 1/(1-1/49)] = -5/49 x 49/48 = -5/48

sum to infinity =7/12 -5/48 =23/48