Basics of Converging Sequences

Algebra Level 1

Find the value of $1 + \dfrac12 + \dfrac14 + \dfrac18 + \dfrac1{16} + \cdots$

2 solutions

Franderly Acosta Valdez
Dec 30, 2015

Let $x=1+1/2+1/4+1/8+...$

$x-1=(1/2)(1+1/2+1/4+1/8...$

$2x-2=x$

$\boxed {x=2}$

Mohammad Khaza
Aug 4, 2017

$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...........$

they are just filling a full number.

so,it will be $1+1=2$

What do you mean by 'filling'

Rishabh Ghosh - 3 years, 10 months ago

suppose, there is a empty anything .then you filled half of it,then quarter of it. if you do this continuously it will

fill the full thing , i actually meant that.

Mohammad Khaza - 3 years, 10 months ago