Ifn=1yn is convergent, thenn=1(1)nyn is also convergent.

Prove that it is false, provide a counterexample.

Let ynod 21 170 , zyn is convergent sequence . (1 ) " syn putting yn , we get ! - - - Now ; let's consider the absolute value of each term In the serves The absolute value of each term in the belies is equal to Jog which is divergent serves . It is harmonic serves with pad . Therefore , ? (-I)" Syn does not converge