Solution of Problem 4 - n-th Term Test
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
®
¥
2
n
n+1
=
¥
¹
0.
Therefore, by the the series diverges.
Note that this problem can also be solved using the
Ratio Test
.