Exercises relating to the integral test.

The function is decreasing for (if the function is not ultimately decreasing, enter
N/A). The integral test doesdoes not
apply to the series The series convergesdivergescan’t be determined using this
test
.

The function is decreasing for (if the function is not ultimately decreasing, enter
N/A). The integral test doesdoes not
apply to the series We have so the series convergesdivergescan’t be
determined using this test
.

The function is decreasing for (if the function is not ultimately decreasing, enter
N/A). The integral test doesdoes not
apply to the series We have that so the series convergesdivergescan’t be
determined using this test
.

The integral test doesdoes not
apply to the series The series convergesdivergescan’t be determined using this
test
.

The integral test doesdoes not
apply to the series The series convergesdivergescan’t be determined using this
test
.

The integral test doesdoes not
apply to the series The series convergesdivergescan’t be determined using this
test
.

The function is decreasing for . By the integral test, We can approximate the
infinite series by the sum of the first seven terms with what bounds on the error?

Using the integral test, we can determine that the sum of the series is equal togreater thanless than
.

### Sample Quiz Questions

When approximating the sum of the infinite series by the sum of the first terms, how large must be to ensure that the approximation error is less than ? Choose the smallest correct bound among those listed.

Because the terms are positive and decreasing, we know that the partial sums are
always less than or equal to the sum of the series. By the Integral Test, we can
further say that To be certain that the error is less than , we set , which gives .