- #1

esuahcdss12

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I need to prove that the limit of the sequence is as shown(0):

1.limn→∞ n*q^n=0,|q|<1

2.limn→∞ 2*n/n!

but I need to do this using the convergence tests. With the second sequence I tried the "ratio test", and I got the result

limn→∞ 2/n+1

which means that L in the ratio test is 0 and so it proves that the sequence converges, but how now should i prove that the limit is indeed 0? I can't use the L'Hopital's rule.

and for the first sequence I am not sure where to start.

can you help please?

1.limn→∞ n*q^n=0,|q|<1

2.limn→∞ 2*n/n!

but I need to do this using the convergence tests. With the second sequence I tried the "ratio test", and I got the result

limn→∞ 2/n+1

which means that L in the ratio test is 0 and so it proves that the sequence converges, but how now should i prove that the limit is indeed 0? I can't use the L'Hopital's rule.

and for the first sequence I am not sure where to start.

can you help please?

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