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## Homework Statement

1 + 1/4 + ... 1/n

^{2}< 2 - 1/n

For n>=2

## Homework Equations

## 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!