no it wont work. the p series test only works when the denominator is n raised to a power 1/n or 1/n^2 or 1/n^(3/2)

even when you indirectly use the p series test with direct comparison or limit comparison an must still be in the form of 1/n

the integral test works the integral 1/(x+1)^2 ,x,0,infinity converges thus the series converges ... the sum however is not found that way.