Test the series for convergence or Divergence 25 46 67 88

Solution

a_n=(-1)ⁿ2ⁿ/(n+4),

|a_n+1/a_n|={2ⁿ⁺¹/(n+5)}/{2ⁿ/(n+4)}|=2(n+4)/(n+5)=2(1+4/n)/(1+5/4) as n gets large this gets close to 2

so the alternating series does not converge