Thread: Sequence converging to Zero.

a) Suppose that (xn)n=1 to infinity is a sequence, and that for all n > 100 we have xn = 1/n. Prove

that xn converges to zero.

b).Now suppose that (xn)n=1 to infinity is any sequence that converges to zero and that (yn)n=1 to infinity is a sequence. Further, suppose that yn = xn for all n > 100. Prove that yn converges to zero. How do i answer this part?
I think the proof for the above part b) is similiar to part a) since yn = xn?

for a) choose any (thanks to tonio this forum)

Thank you for any help in advance.

Originally Posted by charikaar

a) Suppose that (xn)n=1 to infinity is a sequence, and that for all n > 100 we have xn = 1/n. Prove

that xn converges to zero.

b).Now suppose that (xn)n=1 to infinity is any sequence that converges to zero and that (yn)n=1 to infinity is a sequence. Further, suppose that yn = xn for all n > 100. Prove that yn converges to zero. How do i answer this part?
I think the proof for the above part b) is similiar to part a) since yn = xn?

for a) choose any (thanks to tonio this forum)

Thank you for any help in advance.

Yes, it is the same as with (a) because, as it was already pointed, it never mind, for convergence or divergence purposes, if you throw away a finite number of elements of a sequence.

Tonio