sequencies + series

Question 1

where does ncr come from

Answer 1

Question 2

solve ncr equations

Answer 2

 cancel out n! in numerator
 multiply by largest n denominator
 (n-4)! > (n-6)!
 Simplify

Question 3

finding coefficient

Answer 3

List out all possible combinations

Question 4

approximating using binomial expansion

Answer 4

MAKE SURE IT IS IN RANGE OF VALIDITY

Question 5

 Further binomial expansion

Answer 5

Question 6

 Range of validity

Answer 6

Question 7

 Limits of recurrence relationships

Answer 7

Question 8

• Sigma notation

Answer 8

Question 9

Series

Answer 9

sum of consecutive terms of a sequence

Question 10

nth term - arithmetic

Answer 10

Question 10

proof of arithmetic series

Answer 10

Question 11

geometric nth term

Answer 11

Question 12

proving geometric series

Answer 12

Question 13

proving sum to infinity formula

Answer 13

Question 14

 Condition for geometric series to be converging

Answer 14