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

Question

Consider the geometric series 
sin(2x) + sin(2x)cos(2x) + sin(2x)cos^2(2x)
for 0<x< pi/2

(a) Show that the limiting sum S of the series exists
(b) Show that S = cotx

turingtest · Answer

do you know the formuala for a geometric sum?

butterflydreamer · Answer

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

turingtest · Answer

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

turingtest · Answer

what is $r$ in your case?
is $|r|<1$    ?

butterflydreamer · Answer

r would be cos2x .. i think ?

turingtest · Answer

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

butterflydreamer · Answer

-1<r<1 ?

turingtest · Answer

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   ?

butterflydreamer · Answer

yes!

turingtest · Answer

awesome! then we can just plug into our formula for $a$ and $r$

butterflydreamer · Answer

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

turingtest · Answer

you're welcome :)