数学计算题(设元法)(1/11+1/12+1/13+1/14+1/15)*(1/12+1/13+1/14+1/15+1/16)-(1/11+1/12+1/12+1/14+1/15+1/16)*(1/12+1/13+1/14+1/15)
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/28 03:29:50
![数学计算题(设元法)(1/11+1/12+1/13+1/14+1/15)*(1/12+1/13+1/14+1/15+1/16)-(1/11+1/12+1/12+1/14+1/15+1/16)*(1/12+1/13+1/14+1/15)](/uploads/image/z/3862430-62-0.jpg?t=%E6%95%B0%E5%AD%A6%E8%AE%A1%E7%AE%97%E9%A2%98%28%E8%AE%BE%E5%85%83%E6%B3%95%29%281%2F11%2B1%2F12%2B1%2F13%2B1%2F14%2B1%2F15%29%2A%281%2F12%2B1%2F13%2B1%2F14%2B1%2F15%2B1%2F16%29-%281%2F11%2B1%2F12%2B1%2F12%2B1%2F14%2B1%2F15%2B1%2F16%29%2A%281%2F12%2B1%2F13%2B1%2F14%2B1%2F15%EF%BC%89)
数学计算题(设元法)(1/11+1/12+1/13+1/14+1/15)*(1/12+1/13+1/14+1/15+1/16)-(1/11+1/12+1/12+1/14+1/15+1/16)*(1/12+1/13+1/14+1/15)
数学计算题(设元法)
(1/11+1/12+1/13+1/14+1/15)*(1/12+1/13+1/14+1/15+1/16)-(1/11+1/12+1/12+1/14+1/15+1/16)*(1/12+1/13+1/14+1/15)
数学计算题(设元法)(1/11+1/12+1/13+1/14+1/15)*(1/12+1/13+1/14+1/15+1/16)-(1/11+1/12+1/12+1/14+1/15+1/16)*(1/12+1/13+1/14+1/15)
设t=1/12+1/13+1/14+1/15,
则原式=(1/11+1/t)*(1/t+1/16)-(1/11+1/t+1/16)*t=t/11+t^2+1/(11*16)+t/16-t/11-t^2-t/16
=1/(11*16)
(1/11+1/12+1/13+1/14+1/15)*(1/12+1/13+1/14+1/15+1/16)-(1/11+1/12+1/12+1/14+1/15+1/16)*(1/12+1/13+1/14+1/15)=(1/11+1/12+1/13+1/14+1/15)*(1/12+1/13+1/14+1/15)+(1/11+1/12+1/13+1/14+1/15)*(1/16)-(1/11+1/12+1/12+1/14+1/15)*(1/12+1/13+1/14+1/15)-(1/16)*(1/12+1/13+1/14+1/15)=(1/11)*(1/16)=1/176
(1/11+1/12+1/13+1/14+1/15)*(1/12+1/13+1/14+1/15+1/16)-(1/11+1/12+1/12+1/14+1/15+1/16)*(1/12+1/13+1/14+1/15)解答设t=1/12+1/13+1/14+1/15,
则原式=(1/11+1/t)*(1/t+1/16)-(1/11+1/t+1/16)*t=t/11+t^2+1/(11*16)+t/16-t/11-t^2-t/16
=1/(11*16)