There are 8 rows and 8 columns, or 64 squares
on a chessboard. Suppose you place 1 penny on
Row 1 Column A, 2 pennies on Row 1 Column
B, 4 pennies on Row 1 Column C, and so on ...
How many pennies in Row 1?
How many pennies in Row 1-4?
How many pennies on the entire chessboard?

255

4,294,967,295

18,446,744,073,709,551,615

Step-by-step explanation:

Geometric Sequence

Each term of a geometric sequence is obtained by multiplying (or dividing) the previous term by a constant number called common ratio (r). The recursive formula for each term n is

And the general formula is

for n>=1

We place 1 penny on the first cell (square) (row 1, column A). That is the value of a1=1. Now each new cell will have double pennies as much the previous cell. The common ratio is r=2. Thus, the following general formula gives us the number of pennies on the cell n

This gives us the sequence 1,2,4,8,16,32,...,

To get the sum of n terms, we notice the sum forms the sequence 1, 3, 7, 15, 31, 63,... which we can transform as

2-1, 4-1, 8-1, 16-1, 32-1, 64-1,...

Or equivalently

The formula for the sum of n terms is, then

Now we are ready to answer the questions

Row 1 has n=8 cells, thus

The first 4 rows contain 4*8=32 cells, thus

Here n=64

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step-by-step explanation:

what is

step-by-step explanation: