Sequences and series help

• Nov 30th 2011, 03:03 AM
Tweety
Sequences and series help
Imagine a chessboard
suppose 1 grain of corn is placed on the first square.

2 grains on the second
4 grains on the third
8 grains on the fourth

and so on, doubling each time up to and including the 64th square.

1) How many grains would there be on the 64th square?
2) How many would there be on the nth square?
3) How many grains are there on the chessboard?
• Nov 30th 2011, 03:48 AM
e^(i*pi)
Re: Sequences and series help
Quote:

Originally Posted by Tweety
Imagine a chessboard
suppose 1 grain of corn is placed on the first square.

2 grains on the second
4 grains on the third
8 grains on the fourth

and so on, doubling each time up to and including the 64th square.

1) How many grains would there be on the 64th square?
2) How many would there be on the nth square?
3) How many grains are there on the chessboard?

You're doubling each time so you'll get something of the form $2^x$

One our first square (n=1) we've not done any doubling yet so we have $2^0$
One the second square (n=2) we double once $2^1$
One the third square (n=3) we've doubled twice $2^{3-1}= 2^2$

Can you see a pattern?
• Nov 30th 2011, 03:36 PM
CalBear12
Re: Sequences and series help
1. 2^64
2. 2^n
3. 2^64 + 2^63 + ... + 2^0
• Nov 30th 2011, 04:00 PM
skeeter
Re: Sequences and series help
Quote:

Originally Posted by CalBear12
1. 2^64
2. 2^n
3. 2^64 + 2^63 + ... + 2^0

don't think so ...

1. on the 64th square there will be $2^{63}$ grains

2. $2^{n-1}$

3. $\sum_{n=1}^{64} 2^{n-1}$
• Nov 30th 2011, 08:19 PM
CaptainBlack
Re: Sequences and series help
Quote:

Originally Posted by CalBear12
1. 2^64
2. 2^n
3. 2^64 + 2^63 + ... + 2^0

Read the post immediately above yours (by e^(i*pi) ), for a hint about why you are wrong.

CB