Hmm
each term is multiplied by a constant
1/2 times what=-1/4? that is -1/2
-1/4 times what=1/8? that is -1/2
so r=-1/2
does it converge or diverge?
if it converges, it has an infinite sum
if it diverges, it does not
if |r|<1 then it converges
|-1/2|<1?
1/2<1?
true
it converges and has a sum
the sum of an infinite geometric series is
where a1 is the first term and r=common ratio
a1=1/2
r=-1/2
the sum is
each term is multiplied by a constant
1/2 times what=-1/4? that is -1/2
-1/4 times what=1/8? that is -1/2
so r=-1/2
does it converge or diverge?
if it converges, it has an infinite sum
if it diverges, it does not
if |r|<1 then it converges
|-1/2|<1?
1/2<1?
true
it converges and has a sum
the sum of an infinite geometric series is
a1=1/2
r=-1/2
the sum is