Powerpoint Templates Page 1 Powerpoint Templates 1+2=3 (generalized) Math Club 3/19/2012.

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Presentation transcript:

Powerpoint Templates Page 1 Powerpoint Templates 1+2=3 (generalized) Math Club 3/19/2012

Powerpoint Templates Page 2 Definition We should all know that 1+2=3. A polite number is a number that can be written as a sum of positive consecutive numbers. For example, is 22, so 22 is a polite number. Through a few challenges, we will know everything there is to know about polite numbers by the end of this powerpoint.

Powerpoint Templates Page 3 Challenge 1 Show that 3 is a polite number.

Powerpoint Templates Page 4 Challenge 2 Show that 9 is a polite number.

Powerpoint Templates Page 5 Challenge 3 Is 4 a polite number?

Powerpoint Templates Page 6 Challenge 4

Powerpoint Templates Page 7 Challenge 5 Show that all odd numbers are polite.

Powerpoint Templates Page 8 Challenge 6 Show that any number divisible by 3 is polite.

Powerpoint Templates Page 9 Challenge 7 Prove that any number divisible by 7 is polite.

Powerpoint Templates Page 10 Challenge 8

Powerpoint Templates Page 11 Challenge 9

Powerpoint Templates Page 12 Challenge 10 All numbers with an odd factor are polite. What numbers are left?

Powerpoint Templates Page 13 Final Challenge (11) Show that a power of two cannot be polite.