Question

Find s infinite for G.P 1+1/2+1/2^2+.......​

Answer 1

Answer:

answer is 2345

Step-by-step explanation:

2++3=23,23++45=2345

Answer 2

Answer:

The sum of infinite terms of a GP with the first term $a=1$ and the common ratio $r=1/2$ is $S_{} ={2$

Step-by-step explanation:

• For a sequence if the succeeding term is generated from its preceding term by multiplying it with a constant number known as the common ratio such sequences are called

        GEOMETRIC PROGRESSION(GP)

• for example, suppose that $a$ is the first term of a geometric progression with a common ratio $r$ then the sequence is

                         $a,ar,ar^{2},ar^{3},$ etc

• we can calculate the common ratio by taking the ratio of the succeeding number to the preceding number

        ⇒ the common ratio of the above sequence $ar/a=r$

• The sum of infinite terms of a geometric progression is

                       $S_{} =\frac{a}{(1-r)}$ , $0<r<1$

from the question,

The GP is $1+1/2+(1/2)^{2}$

The first term of GP is $a=1$

to find the common ratio take the ratio of the second term to the first term

⇒ the common ratio of GP is $r= \frac{1/2}{1}= 1/2$

substitute these values to get the sum

⇒

$S=\frac{1}{(1-1/2)}=2$