Final answer:
The limit of the expression (2^n + 3^n)^(1/n) as n approaches infinity is found to be 3 using the sandwich theorem, as the expression is squeezed between two other expressions that both converge to 3.
Step-by-step explanation:
The student has asked to find the limit of the expression (2^n + 3^n)^(1/n) utilizing the sandwich theorem. The sandwich theorem, also known as the squeeze theorem, is used to find limits of functions by squeezing them between two other functions that have the same limit at a certain point.
In this case, we know that for all n, 2^n is less than 2^n + 3^n, which in turn is less than 3^n + 3^n, which is 2 * 3^n. Taking the n-th root of each part of the inequality, the expression we are considering is squeezed between 2^(1/n) and (2*3^n)^(1/n). As n approaches infinity, 2^(1/n) approaches 1 and (2*3^n)^(1/n) approaches 3, thus the limit of the given expression is also 3 based on the sandwich theorem.