# Strange infinite series problem using integral test.

1. Apr 14, 2008

### erjkism

1. The problem statement, all variables and given/known data
I need to show that

$$\Sigma\frac{1}{nlnnlnlnn}$$

from n=27 to n=10^(100,000)

is approximately equal to 8.1

2. Apr 14, 2008

### erjkism

i did the u substitution, u =nlnn

and i get

$$\int\frac{1du}{u}$$

which just becomes [lnu]
which becomes: [ln(lnlnn)] evaluated from 27 to 10^100,000

3. Apr 14, 2008

### exk

is the denominator of your summation n*ln(n)*ln(ln(n))?

4. Apr 15, 2008

yea it is