Question

EXERCISE 2.3
Determine whether the sum to infinity of the
following G.P.s exist, if exists find them
i) 1 1 1 1
2'4'8' 16'​

Answer 1

The sum to infinity is "1".

Step-by-step explanation:

The given sequence are

$\dfrac{1}{2} , \dfrac{1}{4}, \dfrac{1}{8}, \dfrac{1}{16}, ......$

Here, first term (a) = $\dfrac{1}{2}$, common ratio(r) = $\dfrac{1}{2}$

The given sequence are in GP.

∴ The sum to infinity = $\dfrac{a}{1 - r}$

= $\dfrac{\frac{1}{2} }{1 - \frac{1}{2} }$

= 1

Hence, the sum to infinity is 1.

You can also see:

https://www.quora.com/How-does-1-2-1-4-1-8-1-16-till-infinity-have-a-sum-2

Answer 2

Answer:

Step-by-step explanation:

The given sequence is 1/2,1/4,1/8,1/16.......

We know a=1/2 and r=1/2

Therefore 1/2 exist in G.P

Sum of infinity =a/1-r .........(formula)

Sum of infinity =1/2/1-1/2

Therefore ,Sum Of Infinity =1.

Hope it's may be helpful.