f(x)=2x/1+2x 求f(1)+f(2).+f(100)+f(1/2)+f(2/2)+...+f(100/2)+.

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  • f(x)=2x/1+2x =4x

    f(1)+f(2).+f(100)=4(1+2+3……100)=4(1+100)*100/2

    f(1/2)+f(2/2).+f(100/2)=4(1/2+2/2+3/2+100/2)=4(1/2+100/2)*100/2

    f(1/3)+f(2/3).+f(100/3)=4(1/3+2/3+3/3+100/3)=4(1/3+100/3)*100/2

    f(1/4)+f(2/4).+f(100/4)=4(1/4+2/4+3/4+100/4)=4(1/4+100/4)*100/2

    s=4*100/2*(1+1/2+1/3+1/4……1/100)+4*100/2(100/1+100/2+100/3+100/4……100/100)

    =200*(1+1/2+1/3+1/4……1/100)+200*100(1+1/2+1/3+1/4……1/100)

    =(200+200*100)*(1+1/2+1/3+1/4……1/100)

    1+1/2+1/3+1/4+.+1/100 =1/1*2+1/2*3+1/3*4+.+1/99*100

    =(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/99-1/100)

    =1-1/100

    =99/100

    s=[200+200*100]*(99/100)=202*99=19998