Could someone please check my work

For each of The following, prove or give a counterexample. 1. If ( s ) converges to s, is it True That ( 1 Sal ) converges to / s/ ? Yes . Ler E DO. Since ( Sn) - 5, INEIN S. T. VnON, Isn-s/ ( 1( - 1) " 1) = ( 1 , 1 , 1 , ... ) - 1 ( ( - 1) " ) = ( - 1 , 1 , - 1 , 1 ,...) diverges First show this ([ Sal ) that is convergent To 1 . Suppose / ( - 1) " / converges . Choose E = 1 , INEIN S.T . VA > N , 116 - 1)9 - 11 = 1 1 - 1 1 = 061. Thus (/ so/ ) converges To 1. Now prove by contradiction That ( S. ) is not convergent. Assume ( Sn) is convergent. Choose E=1. - 3NEIN S.T. VA>N, 1(-1)"- 5/21. When MEN and n is odd, 1 (-1)- - 51 = 1-1- 5/ 0 6 -5