Question

Please help!!!

What is the units digit of 3^1+3^3+3^5 ... 3^2009?

Answer 1

\[3^1 +3^3+ 3^5+3^7 \cdots 3^{2009}\]

Answer 2

Notice that this is

\[\sum_{n = 1}^{2009}3^{2n-1}\]

And by plugging in a few you can notice a pattern:

3 + 27 + 243 +2187 + 19683

the unit of any partial sum alternates from 3 to 0

notice that when n = odd number. the unit of that term is 3
when n = even number, the unit of that term is 7, but when added to the previews gives 0 [from 10]

so is 2009 a term where n is odd or even?

find out:

2n - 1 = 2009

n = 1005 = odd

so the unit of that "partial sum", which is the entire sum is 3

Answer 3

previous* lol

let me know if you have any follow-up questions about by work

Answer 4

oh!!! Thanks!

Answer 5

nope no questions!

Answer 6

glad i could help :)