Question

A few algebra questions (sigmas, sequences, etc.)

(Will post questions in the comments)

Answer 1

"Which represents the series using sigma notation?"\[1, \frac{ 1 }{ 3 }, \frac{ 1 }{ 9 }, \frac{ 1 }{ 27 }\]A.\[\sum_{i=1}^{4}(\frac{ 1 }{ 9 })^{i-1}\]B.\[\sum_{i=1}^{4}\frac{ 3 }{ i }\]C.\[\sum_{i=1}^{4}(\frac{ 1 }{ 3 })^{i+1}\]D.\[\sum_{i=1}^{4}(\frac{ 1 }{ 3 })^{i-1}\]

Answer 2

any guesses?

Answer 3

looks like the denominator is powers of 3, which really only leaves the last two

Answer 4

I tried plugging the numbers in and seeing if any of them matched the series but I must be doing something wrong because I can't figure it out

Answer 5

okay lets try the last two, ignore the first two

Answer 6

\[\sum_{i=1}^{4}(\frac{ 1 }{ 3 })^{i+1}\] put \(i=1\) and get \((\frac{1}{3})^{1+1}=(\frac{1}{3})^2=\frac{1}{9}\) as the first term

Answer 7

you see right away it is wrong, because the first term should be \(1\) not \(\frac{1}{9}\)

Answer 8

Yes, I follow you, so would it be D?

Answer 9

now we can try
\[\sum_{i=1}^{4}(\frac{ 1 }{ 3 })^{i-1}\]

Answer 10

put \(i=1\) and get \((\frac{1}{3})^{1-1}=(\frac{1}{3})^0=1\) so this looks more promising

Answer 11

yes, it is D
you can check it works for \(i=2, 3, 4\) also

Answer 12

is that it?

Answer 13

Thank you very much! Yes, that's it. (:

Answer 14

yw