1/1*2+1/2*3+1/3*4+1/4*5+...+1/199*200

1/1*2+1/2*3+1/3*4+1/4*5+...+1/199*200
1/1*2+1/2*3+1/3*4+1/4*5+...+1/199*200

1/1*2+1/2*3+1/3*4+1/4*5+...+1/199*200
1/1*2+1/2*3+1/3*4+1/4*5+...+1/199*200
= (1- 1/2 )+(1/2- 1/3)+(1/3- 1/4)+.+(1/198-1/199)+(1/199-1/200)
= 1-1/2 +1/2-1/3+1/3-1/4+.+1/199-1/200
= 1- 1/200
= 199/200
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解1/1*2+1/2*3+1/3*4+1/4*5+...+1/199*200
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+...(1/198-1/199)+(1/199-1/200)
=1/1-1/200
=199/200

1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+…+1/(199*200)=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+…+(1/199-1/200)=1-1/200=199/200