Check Recurrence Relation

The formula 1+r+r^2+...+r^n=(r^(n+1)-1)/(r-1) is true for all real numbers r except r=1 and for all integers n>=0. Use this fact to solve the following problem:

If n is an integer and n>=1, find a formula for the expression

2^n-2^(n-1)+2^(n-2)-2^(n-3)+...+((-1)^(n-1))(2)+(-1)^n.

For the values of r and n, I substituted r=(-2) and n=n-1 and got

((2^n)-1)/3.

Did I use the correct substitutions?

Re: Check Recurrence Relation

Quote:

Originally Posted by

**lovesmath** The formula 1+r+r^2+...+r^n=(r^(n+1)-1)/(r-1) is true for all real numbers r except r=1 and for all integers n>=0. Use this fact to solve the following problem:

If n is an integer and n>=1, find a formula for the expression

2^n-2^(n-1)+2^(n-2)-2^(n-3)+...+((-1)^(n-1))(2)+(-1)^n.

For the values of r and n, I substituted r=(-2) and n=n-1 and got

((2^n)-1)/3.

Did I use the correct substitutions?

Now apply the given formula to the expression in square brackets.

CB