“*”表示一种运算符号,它的含义是:x*y=1/xy + 1/(x+1)(y+A);已知2*1=2/3,求198*199的值
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![“*”表示一种运算符号,它的含义是:x*y=1/xy + 1/(x+1)(y+A);已知2*1=2/3,求198*199的值](/uploads/image/z/2433731-59-1.jpg?t=%E2%80%9C%2A%E2%80%9D%E8%A1%A8%E7%A4%BA%E4%B8%80%E7%A7%8D%E8%BF%90%E7%AE%97%E7%AC%A6%E5%8F%B7%2C%E5%AE%83%E7%9A%84%E5%90%AB%E4%B9%89%E6%98%AF%3Ax%2Ay%3D1%2Fxy+%2B+1%2F%28x%2B1%29%28y%2BA%29%3B%E5%B7%B2%E7%9F%A52%2A1%3D2%2F3%2C%E6%B1%82198%2A199%E7%9A%84%E5%80%BC)
“*”表示一种运算符号,它的含义是:x*y=1/xy + 1/(x+1)(y+A);已知2*1=2/3,求198*199的值
“*”表示一种运算符号,它的含义是:x*y=1/xy + 1/(x+1)(y+A);已知2*1=2/3,求198*199的值
“*”表示一种运算符号,它的含义是:x*y=1/xy + 1/(x+1)(y+A);已知2*1=2/3,求198*199的值
2*1 = 1/2*1 + 1/(2+1)(1+A) = 2/3
A = 1
所以198*199 = 1/198*199 + 1/199*200 = 1/198 - 1/199 + 1/199 - 1/200 = 1/198 - 1/200 = 1/19800
2*1 = 1/2*1 + 1/(2+1)(1+A) = 2/3
A = 1
所以198*199 = 1/198*199 + 1/199*200 = 1/198 - 1/199 + 1/199 - 1/200 = 1/198 - 1/200 = 1/19800
2*1 = 1/2*1 + 1/(2+1)(1+A) = 2/3
A = 1
所以198*199 = 1/198*199 + 1/199*200 = 1/198 - 1/199 + 1/199 - 1/200 = 1/198 - 1/200 = 1/19800
2*1=1/1*2+1/(2+1)(1+A)=2/3 A=2
198*199
=1/198*199+1/(198+1)(199+2)
=1/199*(1/198+1/201)
=133/66*199*201
由已知得,1/(2×1)+1/(2+1)(1+A)=2/3 解得A=1
所以198*199=1/(198×199)+1/(198+1)(199+1)
=1/198-1/199+1/199-1/200
=1/198-1/200
=1/19800