Question

Sum of infinite terms of G P 1/2-1/4+1/8-1/16-1/32.. is​

Answer 1

Answer:

Love

Step-by-step explanation:

As with any infinite series, the sum

{\displaystyle {\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{8}}+{\frac {1}{16}}+\cdots }\frac12+\frac14+\frac18+\frac{1}{16}+\cdots

is defined to mean the limit of the partial sum of the first n terms

{\displaystyle s_{n}={\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{8}}+{\frac {1}{16}}+\cdots +{\frac {1}{2^{n-1}}}+{\frac {1}{2^{n}}}}{\displaystyle s_{n}={\frac {1}{2}}+{\frac {1}{4}}+{\frac {1}{8}}+{\frac {1}{16}}+\cdots +{\frac {1}{2^{n-1}}}+{\frac {1}{2^{n}}}}

as n approaches infinity. By various arguments,[a] one can show that this finite sum is equal to

{\displaystyle s_{n}=1-{\frac {1}{2^{n}}}.}{\displaystyle s_{n}=1-{\frac {1}{2^{n}}}.}

As n approaches infinity, the term {\displaystyle {\frac {1}{2^{n}}}}{\displaystyle {\frac {1}{2^{n}}}} approaches 0 and so sn tends to 1.