I know to start out going to the right in direction you assume {Sn} converges. And since it converges for all epsilon>0 there exists an N1 in Natural Numbers such that |Sn1 - L| < epsilon for all n1 greater than or equal to N1.

I know I want to show that for all epsilon>0 there exists an N2 in natural numbers such that |Tn2 - P| < epsilon for all n2 greater than or equal to N2.

I've thought of several ways to approach it. Since it has all the same numbers, the sequences are equal, Tn just reaches the later values of the sequence much quicker. However I do not know how to use that correctly in a proof.

Any help is very much appreciated!!