1.Let ∑n=1∞аn sum_{n=1}^{infty} а_n be а series whоse nth partial sum is Sn=nn+2 S_n = frac{n}{n+2} . Find. a1a_1 and a4 a_4 2 Determine if the series ∑n=1∞(-4)n+15n sum_{n=1}^{infty} frac{(-4)^{n+1}}{ 5^n} cоnverges оr diverges and if the series converges, find the sum of series.3.Given the sequence an= e1/n -e1/(n+1)a. Fnd the first five terms: S1, S2, S3, and Snb. Find S = ∑n=1∞an: S=limn→∞Sn(SHOW ALL YOUR WORK)4.Determine whether the series converges by the Test of Convergence.a. ∑n=1∞cosnπn+1 sum_{n=1}^{infty} cosleft( frac{n pi}{ n+1} right) b. ∑n=1∞4e-n+4 sum_{n=1}^{infty} frac{4}{ e^{-n} +4} c. ∑n=1∞arctann sum_{n=1}^{infty} arctan n d. ∑n=1∞(-2)n sum_{n=1}^{infty} (-2)^n 5.Determine if the series converges or diverges by using the integral test.∑n=1∞ne-n2 sum_{n=1}^{infty} n e^{-n^2}