Hello,

Can you help me with this question -

A positive whole number, greater than 1, is said to be a polite number if it can be expressed as a sum of consecutive whole numbers

eg
6 is polite because it is equal to 1+2+3;
10 is polite because 10=1+2+3+4;

Find all the polite numbers less than 21. Find a pattern in the numbers that are not polite. Explain why every odd number greater than one must be polite.

Thank you

The two polite numbers that you have listed, 6 and 10, can be expressed as a sum of consecutive whole numbers starting at 1. In the defitition of polite numbers there is no requirement that the sum start at 1. In particular, 37 is a polite number since 37 = 18 + 19.

Now try to list all the polite numbers less than 21.

The example I just gave you, 37 = 18 + 19, should be a hint to explaining why every odd number greater than one must be polite.