Question

Find the sum to infinity of the infinite G.P.1-½+¼........​

Answer 1

Answer:

2/3

Step-by-step explanation:

1-1/2+1/4.....

$r=\frac{\frac{-1}{2} }{1} =-\frac{1}{2} \\if~|r|$

Answer 2

Answer:

$\frac{2}{3}$

Step-by-step explanation:

The sum to infinity of a GP is

$S_{infinity}$ = $\frac{a}{1-r}$ ; | r | < 1

where a is the first term and r the common ratio

Here a = 1 and r = - $\frac{1}{2}$ ÷ 1 = - $\frac{1}{2}$ , thus

$S_{infinity}$ = $\frac{1}{1-(-\frac{1}{2}) }$ = $\frac{1}{1+\frac{1}{2} }$ = $\frac{1}{\frac{3}{2} }$ = $\frac{2}{3}$