Hey guys... I just did this question... and I have the solution but I do not understand it still. If someone could just explain what happened.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

1 + 1/4 + ... 1/n^{2}< 2 - 1/n

For n>=2

2. Relevant equations

3. The attempt at a solution

So the base case:

n=2:

1/4 < 2- 1/2, 1/4 < 3/2 True

Suppose this holds for n:

1+ 1/4 +... 1/n^{2}+ 1/(n+1)^{2}< 2 - 1/n + 1/(n+1)^{2}

Here is where I don't understand what happens..

Since 1/n - 1/(n+1) = 1/n(n+1) > 1/(n+1)^{2}, we have 2 - 1/n + 1/(n+1)^{2}< 2 - 1/(n+1).

Then the inequality for n+1 follows.

So I'm confused with why we use 1/n - 1/(n+1).. where did it come from ?

Thanks!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Simple inequality proof by induction

**Physics Forums | Science Articles, Homework Help, Discussion**