For wht values of p does converge

Problem 4EFor what values of p does convergeAnswer;Step-1; 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.Step-2 Now , we have to evaluate for what values of p does dx converges. The P- integrals Consider the function f(x) = (where p> 0) for all xLooking at this function closely we see that f(x) presents an improper behaviour...