The following function 
is defined for all 
, and 
is a positive integer. Prove or provide a counterexample to the following statement.
The convergence of the sequence 
implies the convergence of the integral
![\[ \int_1^{\infty} f(x) \, dx. \]](http://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-0de6fbc486a02589cbcad15bad7a96c6_l3.png "Rendered by QuickLaTeX.com")
Incomplete.
The following function is defined for all , and is a positive integer. Prove or provide a counterexample to the following statement.
The convergence of the sequence implies the convergence of the integral
Incomplete.