Series

Question 1

Find the fraction of

0.676767…

Answer 1

split it up

0.676767 = 0.67 + 0.0067

r = 0.01

S = 0.67 / 1- 0.01 = 67/99.

Question 2

Find the fraction of

0.611111…

Answer 2

split it up

0.611111 = 0.6 + 0.011111

0.011111 = 0.01 + 0.001

r = 0.1

0.01/1-0.1 = 1/90

so

0.611111 = 6/10 + 1/90

times them

550/900

simplify

11/18.

Question 3

a = sqrt(11) and r = sqrt(11)

Answer 3

implementing the formula

sqrt(11) times sqrt(11) ^ n-1

simplify

is sqrt(11)^n

looking for a term like a_5

you sub it in

sqrt(11) * sqrt(11)^5-1

do sqrt(11)^4 = 121

simplify

121sqrt(11)

Question 4

When there is a minus, what should you do?

Answer 4

Always make sure to put things in parentheses in the calculator.

Question 5

How can you find the rate if there is a_4 and a_2 but no a_3?

Answer 5

r^2 = a_4/a_2

then sqrt(ans)

Question 6

Find the sum

1/9 + 5/9 + 5^2 / 9 ….

Answer 6

the sum formula go check whatever

1/9(1-5^n) / 1-5

just simplify it

1/9 times 1/-4

it becomes 1/36 (idk where the minus went)

then overall

1/36 (5^n -1)