Sum to infintiy

1. Jan 10, 2005

Fookie

1+(1/2)+(1/3)+(1/4)+(1/5).........+(1/n)

can sum one prove this series is divergent????????

or just tell me what the expression for sum to infintiy in terms of n is????????

2. Jan 10, 2005

matt grime

replace with a strictly smaller divergent series eg 1+1/2+1/4+1/4+1/8+1/8+1/8+1/8+1/16... or use the integral test.

3. Jan 10, 2005

Fookie

but i thot that the integral test is not valid for series coz the graph of 1/n will not be contiuous

4. Jan 10, 2005

matt grime

I think you ought to look up the integral test and see what it says. The integral test is a perfectly valid way to prove this result.

5. Jan 10, 2005

Rogerio

Forget the first term (1), and observe that:

1/2+1/3 + 1/4+1/5+1/6+1/7 + 1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15 +...>

2*1/4 + 4*1/8 + 8*1/16 +.... =

1/2 + 1/2 + 1/2 +...

Is it enough ?