please help! State why the series the summation from n = 1 to infinity of 5/ 2^(n-1) is convergent or divergent, and if it is convergent, find the sum.

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

answer:

the answer is b) divide by -4 on each side and flip the sign.

step-by-step explanation:

we first need to start by dividing. this is because it is a multiplication problem to start.

we also need to make sure we flip the sign because any time you multiply or divide by negative numbers, the sign must be flipped.

you need to know that the corresponding sides and angles are the same.