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A Level Further Maths Pure 2 > Series > Flashcards

Flashcards in Series Deck (10)
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1

n
Σ ur where un = f(n)-f(n+1)
r=1

f(1) - f(n+1)

2

Solving methods of differences question

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

3

Maclaurin expansion method

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

4

Coefficients of sin and cos in maclaurin

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

5

Using a composite function

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

6

ln of a fraction

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

7

ln of a quadratic

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

8

e^sinx or e^cosx

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

9

When you are expanding ln with the integer not one

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

10

ln(1+sin/cosx)

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