Find the limits of the sequences: 1)b_n=(\frac{3+n}{n})^n 2)a_n=n^{\frac{5}{n}}

plorinosakl

plorinosakl

Answered question

2022-01-25

Find the limits of the sequences:
1)bn=(3+nn)n
2)an=n5n

Answer & Explanation

Kyler Jacobson

Kyler Jacobson

Beginner2022-01-26Added 8 answers

1)bn=(3+nn)n
limnbn=limn(3+nn)n=limn(1+3n)n
We know that
limn(1+an)n=ea
=3e3=20.08
limn(3+nn)n=e3=20.08
2)an=n5n
limnan=limnn5n=limn(n1n)5
=15=1

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