Series expansion, logarithm, coefficients, counterexamples and proof.

[STEP III 2014 Question 1 (Pure)]

Maclaurin, taylor series for trigonometric functions, recurrence, difference equations, comparing coefficients, identity.

[STEP III 2006 Question 3 (Pure)]

Taylor series for tan and cot, recurrence relation, trigonometric identity

[STEP II 1989 Question 2 (Pure)]

Analysis, sum of infinite series, logarithm, exponential function.

[STEP I 1987 Question 4 (Pure)]