Find the sum of the following infinite geometric series, if it exists. ½ + -¼ + ⅛ + -1/16 +

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

The question is kind of confusing. if it's asking how many variations of answers can you give. then do 4^5 for your answer.this would be something like the first question could be a and the 2nd c or first b next c etc. if you can, ask the teacher for a better confirmation of what it's asking. if i'm assuming correctly what it's asking, it's 625 different variations.