Challenge:
$$f(x)=\sum_{n=1}^{infinty}\sin(\frac{2x}{3^n})\sin(\frac{x}{3^n})$$
find f(x) (independent of x) also evaluate the sum of the solutions of the equations f(x)=0 lying in the interval (0,629).

Question

Challenge:
$$f(x)=\sum_{n=1}^{infinty}\sin(\frac{2x}{3^n})\sin(\frac{x}{3^n})$$
find f(x) (independent of x) also evaluate the sum of the solutions of the equations f(x)=0 lying in the interval (0,629).

anonymous · Answer

I didn't make this up I have hundreds of such problems

anonymous · Answer

What book do you have for these?

anonymous · Answer

It is more of uncomplied collection

anonymous · Answer

Any ideas

anonymous · Answer

sin2x = 2cosx*sinx 

But it doesn't seem to work

anonymous · Answer

We shall use transformation formula

anonymous · Answer

cosc + cosd?

anonymous · Answer

sinxsin2x=1/2 (cosx-cos3x)

anonymous · Answer

Oh yeah cosc-cosd, Sorry

anonymous · Answer

You got it!

anonymous · Answer

NotSObright you're so bright! I think we have it now

anonymous · Answer

I know summation formula for cos of angles in AP
not GP

anonymous · Answer

$$f(x) = \cos \frac{x}{3^n} - \cos x, n \to \infty \implies \frac{x}{3^n} \to 0 \implies \cos0 \to 1  $$
$$f(x) = 1-\cos{x}$$

anonymous · Answer

I would like to answer more of such problems

anonymous · Answer

Thanka man

anonymous · Answer

f(x)=(1−cosx)/2

anonymous · Answer

yeah cant forget that 2

anonymous · Answer

Look at the new thread