5

following the formula. Notice that the right-hand side of the formula allows you
to get the answer while avoiding doing the tedious additions of the fractions on
the left-hand side of the equation.)

[With r=1 /2, we have 1

+1

2

=1-

1 2

2

1-1 2for

n=1, and 1

+1

2

+1?

2

?

?
?

2

=1-

1 2

3

1-1 2
for n=2. Verify these and then go ahead and try writing out the formula for
r=1 / 2and n=3.]

1

+r+r

2

+r3

+L+r

n

1-r

=1

-rn+1

1

+r+r

2

+r

3

+L+r

n

=1-rn+1
1-r