Question

Sum to infinite terms of gp 1/2+1/6+1/18+1/54.....

Answer 1

Answer:

answer is 3/4

Step-by-step explanation:

by formula in GP,

sum to infinite terms = a/ 1-r

in the give problem,

a=1/2;

r= t2/t1

=1/6*2/1 =1/3

r= 1/3

therefore , sum of infinite terms = 1/2 /1-1/3

=1/2 /2/3

=1/2*3/2

=3/4

Answer 2

Answer:

The sum to infinite terms of the  GP  $\frac{1}{2} + \frac{1}{6}+ \frac{1}{18} + \frac{1}{54} + ...............$ = $\frac{3}{4}$

Step-by-step explanation:

Given,

The GP  $\frac{1}{2} + \frac{1}{6}+ \frac{1}{18} + \frac{1}{54} + ...............$

To find,

Sum of infinite terms of GP

Solution:

Recall the formula

Sum to infinite terms of a GP =  $\frac{a}{1-r}$ ---------------------(1)

where 'a' is the first term and 'r' is the common ratio of the GP

Here the GP is  $\frac{1}{2} + \frac{1}{6}+ \frac{1}{18} + \frac{1}{54} + ...............$

The first term of the GP = a = $\frac{1}{2}$

Common ratio = $\frac{second \ term }{first\ term}$

= $\frac{\frac{1}{6} }{\frac{1}{2} }$

= $\frac{1}{3}$

∴ The common ratio = r = $\frac{1}{3}$

Substituting the values of 'a' and 'r' in equation (1) we get

Sum of infinite terms of a GP = $\frac{\frac{1}{2} }{1-\frac{1}{3} }$

= $\frac{\frac{1}{2} }{\frac{2}{3} }$

= $\frac{3}{4}$

∴The sum to infinite terms of the  GP   $\frac{1}{2} + \frac{1}{6}+ \frac{1}{18} + \frac{1}{54} + ...............$= $\frac{3}{4}$

#SPJ2