WHAT IS L ALSO TELL ME CHOICE PLZ Consider the series where In this problem you

Question

WHAT IS L

ALSO TELL ME CHOICE PLZ

Consider the series where In this problem you must first attempt to use the Ratio Test to decide whether the series converges absolutely. Compute Leave your answer as a finite number, in f (for + in infinity), - inf (for - infinity ), or DNE if the limit does not exist. Compute the value of L even if the ratio test cannot be applied to this series. L = The Ratio Test says that the series converges absolutely. The series converges absolutely by another test or tests. Neither A nor B is true. Enter the letter for your choice here:

Explanation / Answer

a_(n) = (-1)^(n) * (n!)^2 * 3^(n) /(2n+1)!

replace n with n+1 to get a_(n+1).

a_(n+1) = (-1)^(n+1) * ((n+1)!)^2 * 3^(n+1) /(2n+3)!

now

divide them:

a_(n+1)/a_n = [(-1)^(n+1) * ((n+1)!)^2 * 3^(n+1) /(2n+3)!] / [(-1)^(n) * (n!)^2 * 3^(n) /(2n+1)!]

= -3(n+1)^2 / [(2n+2)(2n+2)]

L = lim n-->infy 3(n+1)^2 / [(2n+2)(2n+2)]

= lim 1/n-->0 3(1+1/n)^2 / [(2+2/n)(2+2/n)]

= 3(1+0)^2 / [(2+0)(2+0)]

= 3 /4

option A)

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