1990/1*2 + 1990/2*3 + 1990/3*4 +...1990/1989*1990 等于多少求简便运算

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1990/1*2+1990/2*3+1990/3*4+...1990/1989*1990等于多少求简便运算1990/1*2+1990/2*3+1990/3*4+...1990/1989*1990等于多

1990/1*2 + 1990/2*3 + 1990/3*4 +...1990/1989*1990 等于多少求简便运算
1990/1*2 + 1990/2*3 + 1990/3*4 +...1990/1989*1990 等于多少
求简便运算

1990/1*2 + 1990/2*3 + 1990/3*4 +...1990/1989*1990 等于多少求简便运算
1990/1*2 + 1990/2*3 + 1990/3*4 +...1990/1989*1990
=1990*(1/1*2+1/2*3+1/3*4+...+1/1989*1990)
=1990*(1-1/2+1/2-1/3+1/3-1/4+...+1/1989-1/1990)
=1990*(1-1/1990)
=1990-1
=1989