Correct answer!

We use the .

For the function

f(x) =

2^x

x+1

we obtain the limit using l'Hopital's Rule:

lim
x® ¥

2^x

x+1

=

lim
x® ¥

e^xln(2)

x+1

=

lim
x® ¥

ln(2)(2^x)

1

= ¥.

Hence

lim
n® ¥

2ⁿ

n+1

= ¥ ¹ 0.

Therefore, by the the series diverges.

Note that this problem can also be solved using the Ratio Test.