1,3,7,15,31 I need a forumlae to fit that series please
That is not the formulae I am looking for. I used that formulae to get these values. also i would like to know how to do part c
The question is:
Let a1;a2;a3; : : : be numbers satisfying the rules that a1 = 1 and
$\displaystyle a_n = 2 a_{n {\color{red}-} 1} + 1$ for all n > 1.
(a) Write down the first few numbers an.
(b) Guess a formula for an.
(c) Prove your guess by induction.
If you're having trouble figuring out how to use the induction-proof technique, try studying a few online articles until you feel more confident.
Then return to this exercise and give it another go. If you get stuck, you will then be able to reply with a clear listing of what you have tried and where you are stuck.
Have fun!