Thread: The Integral Test

Do the series diverge or converge? and why?

1.) n=1 to infinity (5/n+1)

2.) n=1 to infinity (-2/n(square root n))

3.)n=2 to infinity (ln n/(square root n))

4.)n=1 to infinity (1+ 1/n)^n

5.)n=1 to infinity (n/n^2+1)

Originally Posted by TAG16

Do the series diverge or converge? and why?

1.) n=1 to infinity (5/n+1)

2.) n=1 to infinity (-2/n(square root n))

3.)n=2 to infinity (ln n/(square root n))

4.)n=1 to infinity (1+ 1/n)^n

5.)n=1 to infinity (n/n^2+1)

1.



This tends to , and so the series, which is no less than this integral, also tends to . So the series diverges.