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(1+1/2+1/3+...+1/1994)*(1/2+1/3+...+1/1995)-(1-1/2+1/3+..+1/1995)*(1/2+1/3+...+1/1994)怎样算?
题目详情
(1+1/2+1/3+...+1/1994)*(1/2+1/3+...+1/1995)-(1-1/2+1/3+..+1/1995)*(1/2+1/3+...+1/1994)怎样算?
▼优质解答
答案和解析
令 1/2+1/3+...+1/1994 = a
则
(1+1/2+1/3+...+1/1994)*(1/2+1/3+...+1/1995)-(1+1/2+1/3+..+1/1995)*(1/2+1/3+...+1/1994)
= (1+a)*(a+1/1995) - (1+a+1/1995)*a
= (a + a² + 1/1995 + a/1995) - (a + a² + a/1995)
= 1/1995
则
(1+1/2+1/3+...+1/1994)*(1/2+1/3+...+1/1995)-(1+1/2+1/3+..+1/1995)*(1/2+1/3+...+1/1994)
= (1+a)*(a+1/1995) - (1+a+1/1995)*a
= (a + a² + 1/1995 + a/1995) - (a + a² + a/1995)
= 1/1995
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