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- what is the limit of this sequence limn->Infinity (n*sin(π/n))?Show that the infinite sequence 5. an = √ (n2 + 1) − √ (n2 − 1) (n ≥ 1) converges by showing that it is monotone and bounded. You do not need to find the limit of the sequenceShow that the sequence {Sn} give in general terms is convergent.
- Compute the first six terms of the sequence {an} = {n√n}. If the sequence converges, find its limit.Consider the sequence An , whose nth term is given by An = 2(1 + 0.025/n)^n where n is the number of interest payments per year on an initial investment of $2 made at an APR of 2.5%. Determine whether the sequence is convergent or divergent. If it is convergent, find the limit of the sequence and interpret the meaning of the limiting value.In the second sequence, between the second to last line, it looks as though an extra n was pulled out of the limit. Why is that?