8. The series n=1∑∞​np1​ is known as a p-series. Assume that p>0. Use the Integral test to determine values of p for whi

[answerhappygod]

8 The Series N 1 Np1 Is Known As A P Series Assume That P 0 Use The Integral Test To Determine Values Of P For Whi 1 (47.48 KiB) Viewed 32 times

8. The series n=1∑∞​np1​ is known as a p-series. Assume that p>0. Use the Integral test to determine values of p for which the series converges and values of p for which the series diverges. Diverges for p≤1; converges for p>1 9. Consider once again the p-series n=1∑∞​np1​. Remove the restriction p>0. How will the series behave for values of p≤0 ? Explain. The p-series will diverge when p<0 by the divergence test. Thus, we can conclude that the p-series converges for all p>1 and diverges for all p≤1 (not just positive p.)