Question

Calculating sum help? How do I do this?

Answer 1

mhhh

Answer 2

equally, its interesting!we like those questions here!

Answer 3

interpretation: the sum from 1 to infinity of (x)^i

Answer 4

the formula for a geometric sum is\[\sum_{i=0}^\infty ar^i=\frac a{1-r},~if~|r|<1\]notice that your sum starts at \(i=1\), so you will have to subtract off the value of i=0 to use the formula correctly

Answer 5

so what do I use for a?

Answer 6

@TuringTest

Answer 7

what is the coefficient of the part that is being raised to i?

Answer 8

@TuringTest .999

Answer 9

no that is the base that is being raised to i
what is the coefficient of that?

Answer 10

oh, 1000?

Answer 11

compare:\[\sum_1^\infty1000(0.999)^i\\\sum_0^\infty ar^i=\frac a{1-r}\]

Answer 12

yes

Answer 13

so plug in 1000 for a

Answer 14

you need to make the series start at \(i=0\) first

Answer 15

your starts at \(i=1\)

Answer 16

yours*

Answer 17

your series doesn't contain the term for \(i=0\), so you need to add that into the series, and subtract it again at the end
what is the term of the series for \(i=0\) ?

Answer 18

@TuringTest 1?