Unit 8 (Series)

Question 1

What is the formula for the finite sum of an arithmetic series?

Answer 1

n=N
∑(a_n) = ((a_1+a_N)/2)*N
n=1
Where N is the number of terms.

Question 2

What is the formula for the infinite sum of an geometric series?

Answer 2

S=(a_1/(1-r))

Question 3

How does the finite arithmetic formula work?

Answer 3

by adding the two most opposite terms and descending inwards from there…Mr. Freeman’s Leonhard Euler story.

Question 4

How does the infinite geometric formula work?

Answer 4

By multiplying the sum by the denominator of the r value, S can be solved for (see unit 8 note sheet).

Question 5

an infinite geometric formula shows…

Answer 5

…where a series converges.

Question 6

A infinite geometric formula can only work if?

Answer 6

r is greater than -1 and less than 1.

Question 7

What is the formula for the finite sum of an geometric series?

Answer 7

N
∑a_n = a_1(1-r^N)/1-r
n=1

Question 8

How does the finite geometric formula work?

Answer 8

see note sheet

Question 9

Change of base formula

Answer 9

logb(a)=logd(a)/logd(b), take log of base on bottom

Question 10

Setting up compound interest problems:

Answer 10

Mr. O’Hara deposits $120 at the end of each
month into an account that pays 7% interest compounded
monthly.
120(1+0.7/12)

Question 11

What is the formula for the sum of a constant?

Answer 11

N
∑C= Cn
n=1

Question 12

What is the formula for the sum of a line?

Answer 12

N
∑ n=*(1+N)N)/2
n=1

Question 13

What is the formula for a sum of squares?

Answer 13

N
∑ n^2 = (N(N+1)*(2N+6))/6
n=1

Question 14

what is the formula for a sum of cubes?

Answer 14

N
∑ n^3 = (((1+N)N)/2)^2
n=1
it is the sum of lines squared