Assume that the sequence defined by is increasing and an 5

Assume that the sequence defined by is increasing and

a_n < 5

17. 0/2.5 points I Previous Answers Assume that the sequence defined by n 1 5- an is increasing and an 5 for a n. Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) Submit Answer

Solution

Writing down the first few terms of the sequence, we see that

a1 = 1

a2 = 5 - (1/a1) = 5 - (1/1) = 4

a3 = 5 - (1/a2) = 5 - (1/4) = 19/4 = 4.75

a4 = 5 - (1/a3) = 5 - (4/19) = 91/19 = 4.7895

a5 = 5 - (1/a4) = 5 - (19/91) = 436/91 = 4.79

The terms approaches to 5 and hence convergent.

Convergence limit = 5