Series

Question 1

n
Σ ur where un = f(n)-f(n+1)
r=1

Answer 1

f(1) - f(n+1)

Question 2

Solving methods of differences question

Answer 2

Write out the first and last few terms and observe the cancelling to see which terms remain
Likely to need partial fractions to form

Question 3

Maclaurin expansion method

Answer 3

1. Repeatedly differentiate until you reach a cycle or for the amount of terms specified
2. Plug 0 into each
3. Substitute into the Maclaurin expansion formula

Question 4

Coefficients of sin and cos in maclaurin

Answer 4

Use the regular sin and cos expansions and multiply by the coefficients

Question 5

Using a composite function

Answer 5

Substitute in the expression of x - including if it has one power

Question 6

ln of a fraction

Answer 6

Do the ln(numerator) - ln(denominator), remember to subtract 1 for the expression you sub in

Question 7

ln of a quadratic

Answer 7

Factorise and do the sum of each ln, remember to subtract 1 before subbing in

Question 8

e^sinx or e^cosx

Answer 8

Replace sinx and cosx with their expansion and use separate series of e

Question 9

When you are expanding ln with the integer not one

Answer 9

Divide everything inside the ln by that number and put it in front of that but in the ln

Question 10

ln(1+sin/cosx)

Answer 10

Expand sin or cos and separate the lns and use composite functions