Question

show that the series
1+ 1/2 + 1/ 2² +
...+...
converges to 2.​

Answer 1

Explanation:

Find the sum of the infinite series: 1 + 1/2 + 1/2² + 1/2³ + ...

(Hint: Let Sn = 1 + 1/2 + 1/2² + 1/2³ +...+ 1/2^n

Multiply, Sn by 2 to get the following equation:

2Sn = 2 + 1 + 1/2 + 1/2² +...+ 1/2^n + 1/2^(n+1)

Subtract Sn from 2Sn and let Sn tend to infinity to get the sum)