Question

find 1 - 1/2 + 1/2^2 - 1/2^3 + ...​

Answer 1

Answer:

The sum of the infinite series is =2/3

Step-by-step explanation:

The given series is,

1 - 1/2 + 1/2^2 -1/2^3+...

We have to find the sum of the series,

The series can be rewritten as,

1-(1/2) +(1/2) ^2-(1/2) ^3+...

So this is an infinite GP series whose 1st term(a) = 1

And common ratio is(r) = -1/2

That is the mod value of the common ration is less than 1 , so the series is convergent.

So, the sum of the infinite series is = a/(1-r)

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