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A Level Further Maths Pure 2 > Series > Flashcards

Flashcards in Series Deck (10)
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1
Q

n
Σ ur where un = f(n)-f(n+1)
r=1

A

f(1) - f(n+1)

2
Q

Solving methods of differences question

A

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
Q

Maclaurin expansion method

A
  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
Q

Coefficients of sin and cos in maclaurin

A

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

5
Q

Using a composite function

A

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

6
Q

ln of a fraction

A

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

7
Q

ln of a quadratic

A

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

8
Q

e^sinx or e^cosx

A

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

9
Q

When you are expanding ln with the integer not one

A

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

10
Q

ln(1+sin/cosx)

A

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