1. Proof Question

How would I prove that for any a > 1,

1/(a+1) + 1/(a+2) + 1/(a+3) + ... + 1/(a^2) > 1 - (1/a)

2. Originally Posted by thamathkid1729
How would I prove that for any a > 1,

1/(a+1) + 1/(a+2) + 1/(a+3) + ... + 1/(a^2) > 1 - (1/a)
Observer that for $a>1$:

$\dfrac{1}{a+1}\ge \dfrac{1}{a+n}$

where $n$ is a positive integer

3. Originally Posted by thamathkid1729
How would I prove that for any a > 1,

1/(a+1) + 1/(a+2) + 1/(a+3) + ... + 1/(a^2) > 1 - (1/a)
$\displaystyle{\frac{1}{a+1}+\frac{1}{a+2}+\ldots +\frac{1}{a^2}\geq \frac{a^2-a}{a^2}}$

Tonio

4. Found a solution

E=1/(a+1)+1/(a+2)...1/a^2
E>N/(a+1)
N=a^2-a
E>(a^2-a)/(a+1)>(a^2-a)/a^2
I want a real challenge