find the following

bgbgbgbg · Hodge Conjecture Offline Joined: 17 Sep 2009 Posts: 94

find the following
lim[1-cosx cos2x cos3x...cosnx]/x^2 as x goes to 0

**Posted:** Fri Oct 30, 2009 10:48 pm

mavropnevma

Applying l'Hopital yields the limit being $\lim_{x \to 0} \frac {1} {2x} \sum_{k=1}^n \left ( k\sin(kx) \prod_{i\neq k} \cos(ix) \right ) = \frac {1} {2} \sum_{k=1}^n k...$ .

**Posted:** Fri Oct 30, 2009 11:08 pm

_________________
Listen to REMBETIKA for decoding the handle.

bgbgbgbg · Hodge Conjecture Offline Joined: 17 Sep 2009 Posts: 94

thanks. if we want lim{1-(cosx)^2 (cos2x)^2......(cosnx)^n]/x^2 as x goes to 0

**Posted:** Sat Oct 31, 2009 2:20 am

mavropnevma

Assuming that is $\lim_{x \to 0} \frac {1 - \prod_{k=1}^n (cos(kx))^k} {x^2}$ ,

applying l'Hopital yields the limit being $\lim_{x \to 0} \frac {1} {2x} \sum_{k=1}^n \left ( k^2\sin(kx) \cos(kx)^{k-1}\prod_{i\neq k} \cos(ix)^i \right ) = \frac {1} ...$ .

**Posted:** Sat Oct 31, 2009 3:45 am

_________________
Listen to REMBETIKA for decoding the handle.