We know 1 + 1 + 1 + 1 + ..... reaches infinity. So, in a similar way, 0.9 + 0.9 + 0.9 + 0.9 + ...... reaches infinity. What about 1/2 + 1/3 + 1/4 + 1/5 + ....? Do you believe it reaches infinity? If yes, you can ignore the rest of the post. If you want to try it yourself, you can close this page. But if you do not believe it reaches infinity, you are not alone! Warning: This post is about proving the sum as simply as possible. Please don't expect more ;) How do we want to prove it? By comparison. Say we have the value A, with us. Suppose we get another value B, with two conditions:- A > B. B reaches infinity. So, we can conclude A reaches infinity!! Job done. Splitting of our sum for comparing:- Take the first terms of our sum - 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10. Yeah, stop at 1/10. Now, how many terms it has? 9. Now take another sum. 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 (yeah, 9 times). You can be sure about the second sum - I