Find the sum of the numbers from 1 to 100. No calculators allowed! 1+2+3+4+5+6……..+98+99+100 = ?????

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Presentation transcript:

Find the sum of the numbers from 1 to 100. No calculators allowed! …… = ?????

Sigma Notation and The Sum of Natural Numbers Aims: To recognise and be able to use the sum of natural numbers formula. To interpret sigma notation. To apply these to more complex problems.

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Sum of Natural Numbers Animation

Sum of Natural Numbers Formula

Use the formula to help find the sum of: 1)The first 50 natural numbers 2)The first 120 natural numbers 3)The natural numbers between 50 and 100 inclusive. 4)The natural numbers between 100 and 200 inclusive. 5)The sum of the even numbers up to 100. Sum of Natural Numbers Questions

Last n value to use First n value to use SIGMA means (SUM OF TERMS) Nth TERM Formula Sigma Notation Intro

Sigma Notation Examples

Express each of the following as addition sums and find the total where possible. 1) 2) 3) 4) 5) 6) Sigma Notation Questions

Linking the two ideas Usually we will try to use the formula to help find the sum and not list all the terms. We can use the formula to help find the sum for any linear expression. Lets look at some examples.

Examples

A few to try….

Making things a bit harder 1) 2) 3)

Plenary a) Write the series in sigma notation: 1, 4, 7, 10, 13, 16, ……..,1000. b) Find the sum of the series. c) Every third term of the above progression is removed, i.e. 7,16,…. Find the sum of the remaining terms.

Independent Study Further Pure 1 Textbook: Chapter 2 – Series - p14-17 Exercise 2A – p17