# What is the remainder when #1 + x + x^2 + x^3 + ... + x^2006# is divided by #(x-1)# ?

##### 2 Answers

Dec 4, 2016

#### Explanation:

If

In our example:

#f(x) = 1 + x + x^2 + x^3 + ... + x^2006#

So the remainder when dividing by

#f(1) = 1 + 1 + 1 + 1 + ... + 1 = 2007#

Dec 10, 2016

#### Explanation:

or

Making now

so the answer is