Note: The divergence test states if

If the limit of the series is not 0, the series diverges, you can simply take limit here and apply L Hoptials rule since the limit is of indeterminate form here, and notice the limit here is not 0, so it diverges, or you can do as acc100jt did, I know when i have a rational fraction with equivalent degree in denominator and numerator the limit is the ratio of the coefficients. However, but are ways of showing how the limit is not 0.