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 & The Sum of Natural Numbers Lesson 1 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.

Sum of Natural Numbers Thought to be first found by famous mathematician Gauss when he was in school. Demonstration:

Sum of Natural Numbers Formula

Sum of Natural Numbers Questions 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.

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

Sigma Notation Examples

1) 2) 3) Sigma Notation Questions Express each of the following as addition sums and find the total. 3 mins

Linking the two ideas Examples Work out these: (a)(b)(c) Usually we will try to use the formula to help find the sum and not list all the term, as this can be time consuming when n is large. We can use the formula to help find the sum for any linear expression.

A few to try…. 10 minutes

Making things a bit harder Examples Work out these: (a)(b)(c) Do Exercise 2A – p17

Plenary/Extension a) Write the series in sigma notation: 1, 4, 7, 10, 13, 16, ……..,1000. b) Find the sum of the series.