SOLUTION: Give an example of a sequence {an} satisfying that: {an} is monotonic, 0<an<1 for all n and no two terms are equal, lim(n tends to infinity)an = 1/2

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Question 549757: Give an example of a sequence {an} satisfying that:
{an} is monotonic,
0 lim(n tends to infinity)an = 1/2
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
a%5Bn%5D=n%2F%282n%2B1%29 <--> a%5Bn%5D=1%2F2-1%2F2%282n%2B1%29 with a%5B1%5D=1%2F3 and increasing
a%5Bn%5D=%28n%2B1%29%2F%282n%2B1%29 <--> a%5Bn%5D=1%2F2%2B1%2F2%282n%2B1%29 with a%5B1%5D=2%2F3 and decreasing
a%5Bn%5D=1%2F2%2B%281%2F2%29%5E%28n%2B1%29%29 with a%5B1%5D=1%2F2%2B1%2F4=3%2F4 if you want it to converge faster