1. ## [SOLVED] series

1,3,7,15,31 I need a forumlae to fit that series please

2. $\displaystyle {a_1}= 1$ and a(n + 1) = $\displaystyle {a_n} + 2^n$ I think work. I'm a bit sleepy

3. 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.

4. $\displaystyle 2^n - 1$

And n=1

I'm not sure if this is what you're looking for.

5. Originally Posted by ronaldo_07
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
an = 2(an+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.
It would have saved time and effort if you'd given this information in the first place.

And it would help if you gave the correct recurrence relation which I assume is $\displaystyle a_n = 2 a_{n {\color{red}-} 1} + 1$.

6. sorry it was a typo

this infact is what I wanted to show
$\displaystyle a_n = 2 a_{n {\color{red}-} 1} + 1$

7. Originally Posted by ronaldo_07
sorry it was a typo

this infact is what I wanted to show
$\displaystyle a_n = 2 a_{n {\color{red}-} 1} + 1$

8. thanks

9. i have substituted the values n=1,2,3,4,5 to show part c is that correct?

10. Originally Posted by ronaldo_07
i have substituted the values n=1,2,3,4,5 to show part c is that correct?
No. That's not how proof by induction works. Have you been taught proof by induction?

11. yes but it is very confusing how to approach it.

12. for induction I start off with n=0 and see if it still follows the pattern and in this case it dosen't I think. As this would make 2^0-1 = 0

13. Originally Posted by ronaldo_07
yes but it is very confusing how to approach it.
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!