Infinity sum.!!

${ S }_{ \infty }\quad =\quad \frac { a }{ 1\quad -\quad r }$ ${ S }_{ \infty }\quad =\quad \frac { 1 }{ 1\quad -\quad \frac { 1 }{ 2 } } \quad =\quad \frac { 1 }{ \frac { 1 }{ 2 } } \quad =\quad 2$

$A=1+0.5+0.25+...$

$A=1+ \frac{1}{2}+\frac{1}{4}+...$

$2A= 2+1+\frac{1}{2}+\frac{1}{4}+...$

$2A=2+A$

$\rightarrow A=2$

The sum of an infinite geometric series is given by Sum= a/(1-r), where a is the first term and r is the common ratio of each consecutive term. In this case, a = 1 and r = 0.5 So sum= 1/(1-0.5) = 2