22-08-2009 Prove that the sum is not finite

b'coz its a diverging series!!

There was a kinda theorem I don't remember whose.....

The theorem stated that for a decreasing sequence....a necessary condition for its convergence is lim_{n→∞}n.u_n=0.....

Which is not the case over here.....

ln(1+x)=x-\frac{x^{2}}{2}+\frac{x^{3}}{3}-...

\Rightarrow -ln(1+x)=-x+\frac{x^{2}}{2}-\frac{x^{3}}{3}+...

putting x = -1,

we get

-ln(0)=1+\frac{1}{2}+\frac{1}{3}+...

since -ln(0) tends to ∞,
the series is divergent

use this.

t(r) = 1/r = (1/n)/(r/n)
So lim(n→∞)Σtr(r=1 to n) = ∫dx/x (from 0 to 1)
= lnlxl from 0 to 1
= -ln(0)
= ∞