kolejny problem z udowodnieniem tozsamosci!
: 23 paź 2006, o 17:37
Pomozcie udowodnic tozsamosc:
1)
\(\displaystyle{ \frac{1}{2} + \bigsum_{k=1}^{n}coskx = \frac{sin(n + \frac {1}{2})x}{2sin ( \frac{1}{2}) x}\)
2)
\(\displaystyle{ \bigsum_{k=1}^{n}(-1)^{k+1}sinkx= \frac{sin(\frac{1}{2})x - (-1)^n sin(n+ \frac{1}{2})x}{2cos(\frac {1}{2})x}}\)
Z gory wielkie dzieki!
Kajtek
1)
\(\displaystyle{ \frac{1}{2} + \bigsum_{k=1}^{n}coskx = \frac{sin(n + \frac {1}{2})x}{2sin ( \frac{1}{2}) x}\)
2)
\(\displaystyle{ \bigsum_{k=1}^{n}(-1)^{k+1}sinkx= \frac{sin(\frac{1}{2})x - (-1)^n sin(n+ \frac{1}{2})x}{2cos(\frac {1}{2})x}}\)
Z gory wielkie dzieki!
Kajtek
