Which answer represents the series in sigma notation?

1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64

7

a. ∑ 2^j-1

j=1

7

b. ∑ 1/2(j+1)

j=1

7

c. ∑ 1/2 ^j-1

j=1

7

d. ∑ 1/2j+1

j=1

a.for lorena 14 hours makes $126   for 16 hours she makes 144

for julie 6 hours makes $72 for 21 hours its $252

b. julie makes more money than lorena julie makes $12 an hour and lorena makes $9  

.

x^2 + 81

we can factor this using difference of square binomials.

rewrite the equation:

x^2 - (-81)

factor:

(a^2 - b^2) = (√a^2 + √b^2)(√a^2 - √b^2)

(x^2 - (-81) = (x + √-81)(x - √-81)

we can remove the - from under the radical by multiplying it by i.

(x^2 - (-81) = (x + i√81)(x - i√81)

(x^2 - (-81) = (x + 9i)(x - 9i)

we can check our answer by using foil:

x^2 - 9ix + 9ix - 81i^2

x^2 - 81^2

i^2 = -1

x^2 + 81