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?

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 $\displaystyle 2^x$

One our first square (n=1) we've not done any doubling yet so we have $\displaystyle 2^0$

One the second square (n=2) we double once $\displaystyle 2^1$

One the third square (n=3) we've doubled twice $\displaystyle 2^{3-1}= 2^2$

Can you see a pattern?

Re: Sequences and series help

1. 2^64

2. 2^n

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

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 $\displaystyle 2^{63}$ grains

2. $\displaystyle 2^{n-1}$

3. $\displaystyle \sum_{n=1}^{64} 2^{n-1}$

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