Find the first three non-zero terms in the Maclaurin series for $\sin(x)$.

Find the first 3 terms in the MacLaurin series for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.

Binomial series for Natural exponent

Find the first 3 terms of Binomial series having a Natural exponent

Find the nth term of an Arithmetic progression

Find the sum of the first n terms of an arithmetic progression

Find the nth term of a Geometric progression

Solving for a geometric series

Solving for a geometric series

Solving for a geometric series

Binomial series for Natural exponent

Find the first three terms in the binomial series expansion having a non-Natural exponent

Find the first 3 terms of Binomial series having a Natural exponent

Use a series of difference tables to determine the coefficients of a degree three polynomial function from a set of data values, equally spaced over the x-axis.

Calculate a particular harmonic component of the complex form of a Fourier series expansion.

Calculating particular harmonic components of a Fourier series expansion.

Calculating particular harmonic components of a Fourier series expansion.

A question to test integration by parts in a "pre-Fourier series" setting.

Calculating particular harmonic components of a Fourier series expansion.

Multiple response question (4 correct out of 8) covering properties of convergent and divergent series and including questions on power series. Selection of questions from a pool.

Test whether a student knows the root test of a series, and how to use it. Series include those that the root test is inconclusive for. This question could be better in that it could go through the working of determining the limit but I hope to make a separate question which deals with that.

Determine a finite sum and a limiting sum of a geometric series written using sigma notation. I'm not sure how to eliminate rounding errors...

Often students need practice re-indexing series, these are three questions that give them that opportunity.

Test whether a student knows the divergence test of a series, and how to use it. Series include those that the diverence test is inconclusive for. This question could be better in that it could go through the working of determining the limit but I hope to make a separate question which deals with that.

This question tests to see if students can recognise a $p$-series and based on its $p$-value determine if it is convergent or divergent.

This question tests to see if students can recognise a geometric series and based on its common ratio determine if it is convergent or divergent.

This question tests to see if students can recognise an alternating series and based on the alternating series test and the divergence test determine if it is convergent or divergent.

At the moment there is no example included with $b_n\rightarrow 0$ which isn't eventually monotonically convergent. 

Test whether a student knows the ratio test of a series, and how to use it. Series include those that the ratio test is inconclusive for. This question could be better in that it could go through the working of determining the limit but I hope to make a separate question which deals with that.

Test whether a student knows the comparison test of a series, and how to use it. Series include those that the comparison test is inconclusive for.

Solving for a geometric series