作业帮若f(x)=sin(π/6)x,则f(1)+f(3)+f(5)+~~~~ +f(2011)
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若f(x)=sin(π/6)x,则f(1)+f(3)+f(5)+~~~~ +f(2011)
若f(x)=sin(π/6)x,则f(1)+f(3)+f(5)+~~~~ +f(2011)
若f(x)=sin(π/6)x,则f(1)+f(3)+f(5)+~~~~ +f(2011)
f(1)+f(7)
=sin(π/6)+sin(7π/6)
=sin(π/6)+sin(π/6+π)
=sin(π/6)-sin(π/6)
=0
同理
f(3)+f(9)=0
f(5)+f(11)=0
也就是说,每6个数之和为0
原式,从1到2011,共有(2011-1)/2+1=1006个数
1006/6=167.4
原式=f(1)+f(3)+f(5)+f(7)
=f(3)+f(5)
=sin(3π/6)+sin(5π/6)
=1+1/2
=3/2
f(x)=sin(π/6)x
f(1)+f(3)+f(5)+~~~~ +f(2011)
=sin(π/6)+sin(3π/6)+sin(5π/6)+sin(7π/6)+sin(9π/6)+sin(11π/6)+...+sin(2011π/6)
可见每6个的和为0
令2011＝2n-1
解得n=1006
n÷6=167...4
因此，最后的和为...
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f(x)=sin(π/6)x
f(1)+f(3)+f(5)+~~~~ +f(2011)
=sin(π/6)+sin(3π/6)+sin(5π/6)+sin(7π/6)+sin(9π/6)+sin(11π/6)+...+sin(2011π/6)
可见每6个的和为0
令2011＝2n-1
解得n=1006
n÷6=167...4
因此，最后的和为
f(1)+f(3)+f(5)+~~~~ +f(2011)
=sin(π/6)+sin(3π/6)+sin(5π/6)+sin(7π/6)
=sin(π/6)+sin(3π/6)
=3/2
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