The integral test basically says that if the integration from some constant to infinity exists and is defined then the sum of the series from that constant to infinity exists and is defined. All you need to do it take the integration of each series function.

For each of these, we need to use "lim {a->infinity}" since we cannot find the sum or integration "at" infinity.

lim {a->infinity} SUM {n=1 : a} 1/n^4

Now we can change this to an integration

lim {a->infinity} INT {1 : a} 1/n^4

lim {a->infinity} -1/3*1/n^3 from {1 : a}

(-1/3*(0)) - (-1/3*(1)) = 1/3

The integration exists, therefore so does the series sum.

Try doing that with the other problems.