[SOLVED] series

**ronaldo_07** · January 13th 2009, 06:10 PM

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

**MacstersUndead** · January 13th 2009, 06:13 PM

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

**ronaldo_07** · January 13th 2009, 06:17 PM

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
$a_n = 2 a_{n {\color{red}-} 1} + 1$ for all n > 1.

(a) Write down the first few numbers an.

(b) Guess a formula for an.

(c) Prove your guess by induction.

**Cakecake** · January 13th 2009, 07:24 PM

$2^n - 1$

And n=1

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

**mr fantastic** · January 13th 2009, 07:33 PM

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 $a_n = 2 a_{n {\color{red}-} 1} + 1$ .

**ronaldo_07** · January 13th 2009, 07:50 PM

sorry it was a typo

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

**mr fantastic** · January 13th 2009, 07:55 PM

Originally Posted by ronaldo_07

sorry it was a typo

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

Cakecake has correctly answered (b) in reply #4.

Where are you stuck with (c)? Please show your working.

**ronaldo_07** · January 13th 2009, 07:57 PM

thanks

**ronaldo_07** · January 13th 2009, 08:05 PM

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

**mr fantastic** · January 13th 2009, 08:17 PM

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?

**ronaldo_07** · January 13th 2009, 08:18 PM

yes but it is very confusing how to approach it.

**ronaldo_07** · January 13th 2009, 08:24 PM

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

**stapel** · January 14th 2009, 03:44 AM

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!

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