Question

Consider the geometric series
sin(2x) + sin(2x)cos(2x) + sin(2x)cos^2(2x)
for 0 11 years ago

Answer 1

do you know the formuala for a geometric sum?

Answer 2

Is it Sn = a(1-r^n) /1-r ?

Answer 3

for an infinite series it is\[\sum_0^\infty ar^n=\frac a{1-r},~if~|r|<1\]

Answer 4

what is \(r\) in your case?
is \(|r|<1\) ?

Answer 5

r would be cos2x .. i think ?

Answer 6

yes, and is that <1 on the interval (0,pi/2) ?

Answer 7

-1<r<1 ?

Answer 8

that is the requirement to be able to use the formula I gave above
is -1<cos(2x)<1 in the interval 0<x<pi/2 ?

Answer 9

yes!

Answer 10

awesome! then we can just plug into our formula for \(a\) and \(r\)

Answer 11

ohhh okay! I think i understand it now :)
Thank you :D !!

Answer 12

you're welcome :)