Use the sandwich lemma to solve --> Let 0<a<b . The sequence ((a^ n +b^ n )^ 1/n ) converges to b .

Answer 1

Since 0<a<b, it is obvious that b = (bⁿ)^1/n < (aⁿ+bⁿ)^1/n<(2bⁿ)^1/n=2^1/nb. When n→∞, 2^1/n→ 1.