Arithmetico-geometric mean and recurrence: prove the two sequences have the same limits
113125
Arithmetic-geometric Mean
97047
Limit for sequence $a_{m+n}\leq a_m+a_n$
48500
Proof of convergence of sequences
13323
Convergence of the arithmetic mean
16392
Prove the Inequality on sequence
130476
Prove that every terms of a sequence defined by a recurrence relation is a perfect square.
141895
Proving that a sequence is monotone
65168
Proof of sequence inequality
29836
Prove: Convergent sequences are bounded
2092
Convergence of a sequence with assumption that exponential subsequences converge?
88365
Prove the sequence converge and find its limit
44823
Prove the general arithmetic-geometric mean inequality
80542
limit of a geometric mean
61018
prove two dependent sequences converge
70561
limit of the sequence $a_n=1+\frac{1}{a_{n-1}}$ and $a_1=1$
62127
Prove recursively defined sequence converges
14489
Showing that a sequence is monotone and thus convergent