- #1
PhillipKP
- 65
- 0
Homework Statement
This is kind of a question regarding summation.
All logs are to base 2.
Given
[tex]A=\sum_{n=2}^{\infty}(n\log^{2}(n))^{-1}[/tex]
Why does the the Author get
[tex]\sum_{n=2}^{\infty}\frac{\log A}{An\log^{2}(n)}=\log A[/tex]
?
Homework Equations
The Attempt at a Solution
But working it out, I get
[tex]\sum_{n=2}^{\infty}\frac{\log A}{\sum_{n=2}^{\infty}(n\log^{2}(n))^{-1}n\log^{2}(n)}=\sum_{n=2}^{\infty}\frac{\log A}{\sum_{n=2}^{\infty}1}[/tex]
Since [tex]A\approx1.013[/tex]
[tex]log(A)\approx0.019[/tex]
Therefore
[tex]\sum_{n=2}^{\infty}\frac{0.019}{\infty}=0[/tex]
What did I do wrong?
Thanks for any help in advance.