Thread: 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?

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

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

Can you see a pattern?

1. 2^64
2. 2^n
3. 2^64 + 2^63 + ... + 2^0

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 grains

2.

3.

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