1(1/2)+2(1/6)+3(1/12)+4(1/20).20(1/420)=?

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1(1/2)+2(1/6)+3(1/12)+4(1/20).20(1/420)=?1(1/2)+2(1/6)+3(1/12)+4(1/20).20(1/420)=?1(1/2)+2(1/6)+3(1/

1(1/2)+2(1/6)+3(1/12)+4(1/20).20(1/420)=?
1(1/2)+2(1/6)+3(1/12)+4(1/20).20(1/420)=?

1(1/2)+2(1/6)+3(1/12)+4(1/20).20(1/420)=?
=(1+2+3+...+20)+(1/2+1/6+1/12+1/20+...+1/420) =(1+20)*20/2 + [1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+...+1/(20*21)] =210+(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.+1/20-1/21) =210+(1-1/21) =210+20/21