Question

What equation will give the sum of this geometric series?

30 + 3-1 + 3-2 + 3-3 + 3-4 + ⋯ + 3-9

Answer 1

your answer is 32 i believe

Answer 2

could you give me a medal

Answer 3

it's asking for an equation, not a number

let me think about this for a sec

Answer 4

woops

Answer 5

are those supposed to be exponents?

like:

3^0 + 3^(-1) + 3^(-2)...etc

Answer 6

yes

Answer 7

ok, that makes things a lot more clear now :P

first step is to identify the common ratio

if we rewrite the terms as fractions, we can see the pattern more clearly

3^0 + 3^(-1) + 3^(-2) ...

is equal to

1 + (1/3) + (1/9)... with me so far?

Answer 8

yes i think

Answer 9

the pattern is that each consecutive term gets multiplied by (1/3), with me so far?

Answer 10

yah

Answer 11

good.

so the common ratio is (1/3) and the first term is 3^0, which is also equal to 1.

there are 10 terms in the series (0,1,2,3,4,5,6,7,8,9)

Answer 12

so we plug

a = 1
r = (1/3)
n = 10

into this equation: