# Find a general formula ...

• Sep 2nd 2009, 05:58 PM
jaclyn91
Find a general formula ...
Let \$\displaystyle x_1 = 1\$ and \$\displaystyle x_{n+1} = 2x_n + 1, ~ n \geq 1\$.

Find and prove a general formula for \$\displaystyle x_n\$.

Not sure where to start ... Do you solve for \$\displaystyle x_n\$ ?
• Sep 2nd 2009, 07:57 PM
mr fantastic
Quote:

Originally Posted by jaclyn91
Let \$\displaystyle x_1 = 1\$ and \$\displaystyle x_{n+1} = 2x_n + 1, ~ n \geq 1\$.

Find and prove a general formula for \$\displaystyle x_n\$.

Not sure where to start ... Do you solve for \$\displaystyle x_n\$ ?

Have you been taught how to solve difference equations (recurrence relations)?
• Sep 2nd 2009, 08:13 PM
ynj
Quote:

Originally Posted by jaclyn91
Let \$\displaystyle x_1 = 1\$ and \$\displaystyle x_{n+1} = 2x_n + 1, ~ n \geq 1\$.

Find and prove a general formula for \$\displaystyle x_n\$.

Not sure where to start ... Do you solve for \$\displaystyle x_n\$ ?

\$\displaystyle x_{n+1}+1=2(x_n+1)\Rightarrow x_{n}+1=2^{n-1}(x_{1}+1)\$