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fk378

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## Homework Statement

Given the limit (B-->inf) [(lnB)^(-p+1)] / (-p+1) - [(ln1)^(-p+1)] / (-p+1)

For what p does this converge?

## The Attempt at a Solution

For the left side of the minus sign,

if 1-p<0 --> 0

if 1-p>0 --> inf

but for the ln(1) on the right side of the minus sign, ln(1)=0, so it would be

if 1-p<0 then you would get a zero in the denominator (since ln(1) would be raised to a negative power) and therefore ---> inf

if 1-p>0 then you would have zero as the numerator, but be left with infinity as the other value and hence ---> inf

The book says that for p>1 then it will converge. But how can that be, if you'll end up with a negative exponent for the 0??

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