Summing an Infinite Series: Can We Prove Divergence?

[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?

 

[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.

 

[Fookie]

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

 

[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.

 

[Rogerio]

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

can sum one prove this series is divergent?

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 ?