Find a general formula ...

**jaclyn91** · September 2nd 2009, 05:58 PM

Let $x_1 = 1$ and $x_{n+1} = 2x_n + 1, ~ n \geq 1$ .

Find and prove a general formula for $x_n$ .

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

**mr fantastic** · September 2nd 2009, 07:57 PM

Originally Posted by jaclyn91

Let $x_1 = 1$ and $x_{n+1} = 2x_n + 1, ~ n \geq 1$ .

Find and prove a general formula for $x_n$ .

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

Have you been taught how to solve difference equations (recurrence relations)?

**ynj** · September 2nd 2009, 08:13 PM

Originally Posted by jaclyn91

Let $x_1 = 1$ and $x_{n+1} = 2x_n + 1, ~ n \geq 1$ .

Find and prove a general formula for $x_n$ .

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

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

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