\fExercise. One of the major consequences of this is that multiplying or dividing a given sequence by a polynomial will not affect the limit required in the Ratio Test. Indeed, consider the series 22:1 Elk Note that this is a geometric series, but we could establish its convergence using the Ratio Test. Indeed, here: Lliin new an, new 2+1 Now, let's multiply the original sequence dened by the rule an 2 (%)n by the polynomial p(n) = n5 and try to sum its terms. 5 That is, we want to consider the series 22:1 i\" We nd: 5 n. n 5 , 5 Llim (n+1) -2 lim 2 -(\"+51)_n*2)'.((n+ \\ (Tl+1) n 71)00 2n+1 \