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Çócosx+cos2x+cos3x+¡­+cosnxµÄÖµ.Óø´ÊýµÄ·½·¨¼ÆËã...

³ËÒÔ2sinx,»ý»¯ºÍ²î¾Í±ä³ÉÁË sin2x-0+sin3x-sinx+sin4x-sin2x+...+sinnx-si(n-2)x+sin(n+1)x-sin(n-1)x=sin(n+1)x+sinnx-sinxÔÙ³ýÒÔ2sinx,¼´Îª´ð°¸.


...Ö¤Ã÷:sinx+sin2x+sin3x+¡­¡­+sinnx=[sin(nx/2)sin((n...

=[sin((n-1)x/2)sin(nx/2)+sinnxsin(x/2)]/sin(x/2)=sin(nx/2)[sin((nx/2-x/2)+2cos(nx/2)sin(x/2)]/sin(x/2) ʹÓÃÁËsinnx=2sinnx/2...


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ÇëÎÊһϸ÷λ´óÀÐÕâÌâÔõô×ö?Çó¡Òsin2nx/ sinx dx(n=1...

n+1)xsin2nxsinxdx=2¡Òcos(2n+1)xdx=2sin(2n+1)x2n+1+Cn,ËùÒÔAn=¡Æk=0n12sin(2k+1)x2k+1+C.


sin2nx/sinxµÄ²»¶¨»ý·ÖÔõôÇó,»¹ÓÐÎÒ¿´ÍøÉϵĹý³ÌͼÖÐÕâ²½ÊÇ...

¾ßÌ廨´ðÈçÏ£ºsin2nx=sin(2n-1)xcosx+cos(2n-1)xsinx =1/2(sin2nx+sin(2n-2)x)+cos(2n-1)xsinx ¡à¡Ò(sin2nx/sinx)dx=1/2...


Çó¡Ò(0,¦Ð)x2*sin(nx)µÄ»ý·Ö

Çó¡Ò(0,¦Ð)x2*sin(nx)µÄ»ý·Ö ThyFhw


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