Y1, C3 - Series

Question 1

What is the sum of 5 from r = 1 to n

Answer 1

5n

Question 2

What is the sum of the first n natural numbers

Answer 2

0.5n (n + 1)

Question 3

How to solve the sum of r from r = 21 to 50

Answer 3

Subtract the (sum of r from r = 1 to 20) from (the sum of r from r = 1 to 50)

Question 4

How to factorise ac + ad + bc + bd

Answer 4

= (a + b)(c + d)

Question 5

Factorise (2n + 4)(n - 1) - (n - 3)(n - 1)

Answer 5

= (n - 1)[2n + 4 - (n - 3)]
= (n - 1)(n + 7)

Question 6

What does the number above sigma mean in sigma notation

Answer 6

The ending number

Question 7

What does x in r = x mean in sigma notation

Answer 7

The starting number

Question 8

Can you have non-integers above or below the sigma notation (starting or ending number)

Answer 8

NO

Question 9

Express 25 + 15 + 5 - 5 in sigma notation

Answer 9

r = 1, ending at 4, expression being summed = (35 - 10r)

Question 10

What is the sum of r from r = 5 to 2N - 1

Answer 10

= sum of r from r = 1 to 2N - 1 - (sum of r from r = 1 to 4)
Formula: 0.5n(n+1)
= 2N^2 - N - 4 - (6)
= 2N^2 - N - 10

Question 11

How can the sum of (3r + 4) from r = 1 to 13 be broken up

Answer 11

= 3 * (sum of r from r = 1 to 13) + (sum of 4 from r = 1 to 13)
= 325

Question 12

What is the sum of squares

Answer 12

= 1/6 * n * (n+1)(2n+1)

Question 13

What is the sum of cubes

Answer 13

= 1/4 * n^2 * (n+1)^2

Question 14

What is n in sigma notation

Answer 14

The ending number

Question 15

What is r in sigma notation

Answer 15

The expression being summed

Question 16

If you cancel a solution by (n+1), what solution are you cancelling

Answer 16

n = -1

Question 17

Why can’t n = -ve numbers in sigma notation

Answer 17

You cannot go backwards when summing numbers (cannot go from r = 1 to -5)