Solution Found!
For wht values of p does converge
Chapter 7, Problem 4E(choose chapter or problem)
For what values of p does \(\int_{1}^{\infty} x^{-p} d x\) converge?
Questions & Answers
QUESTION:
For what values of p does \(\int_{1}^{\infty} x^{-p} d x\) converge?
ANSWER:Step 1 of 6
Definition ;
The partial sum of the series is given by
= + ++..............+ . If the sequence of these partial sums {Sn} converges to L,
then the sum of the series converges to L. If {Sn} diverges, then the sum of the series diverges.
= is convergent . Conversely , a series is divergent if the sequence of partial sums is divergent. If and are convergent series , then + ) and - ) are convergent . If C , then is convergent series.
NOTE : The terms grow without bound , so the sequence does not converge.
Integral test ; The series can be compared to an integral to establish convergence or divergence.
Let f(n) = be a positive monotone decreasing function . If
f(x) dx = f(x) dx < ,
then the series converges. But if the integral diverges, then the series does so as well.