# Math Help - 1/2 + 2/3 + 3/4 + 4/5+..............?

1. ## 1/2 + 2/3 + 3/4 + 4/5+..............?

1/2 + 2/3 + 3/4 + 4/5+.............?

2. ## Re: 1/2 + 2/3 + 3/4 + 4/5+..............?

Originally Posted by AaPa
1/2 + 2/3 + 3/4 + 4/5+.............?
What you have is $\sum\limits_{k = 1}^\infty {\frac{k}{{k + 1}}}$ and you know that $\left( {\frac{n}{{n + 1}}} \right) \to 1$ SO?

3. ## Re: 1/2 + 2/3 + 3/4 + 4/5+..............?

It is divergent as any partial sum Sn of this series is greater than the coresponding sum of the Harmonic series Σ(1/n) which is divergent.

4. ## Re: 1/2 + 2/3 + 3/4 + 4/5+..............?

One of the first things most people learn about infinite sums is:
If $\sum a_n$ converges then \lim_{n\to \infty} a_n= 0[/tex].

Here, $a_n= \dfrac{n-1}{n}$ which does NOT go to 0.