Does Convergence of (sn) and (sntn) Imply (tn) Converges?

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The discussion centers on proving the convergence of the sequence (tn) given that (sn) converges to a non-zero limit s and (sntn) converges to L. The participants emphasize the importance of the algebraic limit theorem in analyzing the relationship between the sequences. Specifically, they suggest exploring the implications of the convergence of (sn) and (sntn) on the behavior of (tn) through algebraic manipulation.

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gsmith89
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Hello was wondering if anyone could help me prove that:
Suppose (sn) converges to s not equal to 0 and ( sntn) converges to L. Prove that (tn) converges
 
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gsmith89 said:
Hello was wondering if anyone could help me prove that:
Suppose (sn) converges to s not equal to 0 and ( sntn) converges to L. Prove that (tn) converges

Hello gsmith89 and welcome to the forums.

What can you say about sn, tn, and sntn in relation to (sn + tn)^2?
 
Have you looked at the algebraic limit theorem?
 

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