Question

Does the following series converge or diverge?

Σ
n=1
4
8√n +7³√n
O The series diverges.
O The series converges.

Answer 1

converges

Explanation:

the individual fraction terms go against 0 with larger and larger n.

and therefore the sum converges.

the numerator of the fractions stays constant (4) but the denominator (bottom) of the fraction increases more and more with investing n (it does not matter that it uses roots, compared to the constant 4 they too grow immensely large with large n).

the limit of a/infinity is defined as 0.