Summation Of Series

Question 1

What are the different part of the sigma function called?

Answer 1

The number above the sigma is the ending term
The number below the sigma is the starting term
The equation to the right of the sigma is the rule

Question 2

What is the equation for a sigma function with the a rule consisting of a only a number?

Answer 2

x * n

Where ‘x’ is the rule and ‘n’ is the ending term

Question 3

What is the equation for a sigma function with ‘r’ ?

Answer 3

1/2(n)(n+1)

Question 4

What is the equation for a sigma function with ‘r²’ ?

Answer 4

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

Question 5

What is the equation for a sigma function with ‘r³’ ?

Answer 5

1/4(n²)(n+1)²

Question 6

How to work out the sigma function when the starting term is n+1?

Answer 6

You take the sigma function with the same ending term and the starting term at 1. Then you subtract ‘n’ as the ending term and the starting term at 1

Question 7

How to work out the sigma function with the starting term over 1?

Answer 7

You take away a sigma function with the ending term one less than the starting term of the sigma function being calculated and the starting term as one. This is taken from a sigma function with the same ending term and the starting term at 1

Question 8

What is the method of differences?

Answer 8

Used in the summation of series, methods of differences splits the rule into different parts which can be cancelled out to simplify the calculation of the answer

Question 9

What is proof by induction?

Answer 9

Proving two sides of an equation are equal for all values of a variable. This is done by proving the property is true for a starting point and then proving it is true for all numbers greater than the starting point

Question 10

What are the steps to the proof by induction?

Answer 10

Basis: Prove the general statement is true for n=1
Assumption: Assume the general statement is true for n=k
Induction: Show that the general statement is true for n=k+1
Conclusion: The general statement is then true for all positive integers of ‘n’

Question 11

What should the conclusion read every time?

Answer 11

Since true for n = 1 and if true for n = k, true for n = k+1, therefore true for all of n