What is the sum of series 1/2+1/4+1/6+… up to infinity?

Question

So someone told me its infinity, but i don't get it

it sure looks like its just keep getting smaller and smaller so how is this going to infinity? or is it?

I know that 1+1/2+1/4+1/8+... is 1 so how is this infinity?

Answer 1

$$ \dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{6}+\dfrac{1}{8}+\cdots=\dfrac{1}{2}\left(1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+\cdots\right) $$

Answer 2

No, sorry. Note that the sum: $$S = 1 +\frac12 +\frac14 + \frac18 +\ldots$$ converges to $\color{red} 2$. A typo perhaps?

Now, the sum: $$S = \frac12 + \frac14+\frac16+\ldots$$ $$= \frac12 \left[1 + \frac12 + \frac13 + \ldots \right] $$ $$= \frac12 S_1$$ where $S_1$ diverges as was shown here on MSE earlier.