Question

lim n -1/0 ( 1/2+ 1/4+1/8 ...........+1/2^n)​

Answer 1

$answer \\ \\ lim \: \: \: \: \: \: \: \: ( \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + ... + \frac{1}{2 {}^{n} }) \\ n - \infty \\ \\ lim \: \: \: \: \: \: \: \: \: \frac{ \frac{1}{2}( 1 - \frac{1}{2 {}^{n} } )}{ 1 - \frac{1}{2} } \\ n - \infty \\ \\ becoz \: \: the \: \: above \: series \: is \: in \: g.p \\ \\ lim \: \: \: \: \: \: \: \: \: ( \frac{1}{2 {}^{n} } - 1) \\ n - \infty \\ \\ = (0 - 1) \\ \\ = - 1$