Question

(n+1)/n is a sequence . find its least upper bound.
a)1 b)2​

Answer 1

Answer:

The sequence x is increasing, so it is sufficient to prove for a subsequence of x. For each power p of 10, n = 10^p-1 let x(p) = 1 - 10^-p. M<1 and 1-M >0. The subserie x(p) converges to 1, and the sequence is monotonus, so converges like the subsequence. So there is a p such that 1> x(p) > 1- (1-M)=M