Question

Use the integral test to determine the convergence or divergence of the series.

Answer 1

\[\sum_{}^{\infty} \frac{\ln(n)}{n^{10}}\]

Answer 2

so if it's an integral iut's going to be .

Answer 3

\[\int\limits_{2}^{\infty} \ln(x)/x^{10}\]

Answer 4

\[\int\limits_{2}^{\infty} \ln(x) * \frac{1}{x^{10}}\]

Answer 5

solve for it

Answer 6

u = ln(x)
du = 1/x dx

Answer 7

dv = 1/x^10
v = -1/9x^9

Answer 8

ok now integration by parts.

Answer 9

\[-\frac{\ln(x)}{9x^9} +\frac{1}{9} \int\limits \frac{1}{x^{10}}dx\]

Answer 10

\[-\frac{\ln(x)}{9x^9} +\frac{1}{9} * -\frac{1}{9x^{9}} + c\]

Answer 11

evaluate it at the limits