rosi小莉写真吧:求助:解方程(初二)
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1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+1994)(x+1995)=(2x+3987)/(3x+5985)
1/(x+1)(x+2)= 1/(x+1) - 1/(x+2)
1/(x+2)(x+3)= 1/(x+2) - 1/(x+3)
................
1/(x+1994)(x+1995)= 1/(x+1994) - 1/(x+1995)
所以
1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+1994)(x+1995)=1/(x+1) - 1/(x+1995)=1994/(x+1)(x+1995)
两边都乘以(x+1995),得
3*1994/(x+1)=2x+3987
x=1/2
你们初二就要学到大学里的微积分了?晕的
1/(x+1)(x+2)= 1/(x+1) - 1/(x+2)
1/(x+2)(x+3)= 1/(x+2) - 1/(x+3)
................
1/(x+1994)(x+1995)= 1/(x+1994) - 1/(x+1995)
所以
1/(x+1)(x+2)+1/(x+2)(x+3)+...+1/(x+1994)(x+1995)=1/(x+1) - 1/(x+1995)=1994/(x+1)(x+1995)
两边都乘以(x+1995),得
3*1994/(x+1)=2x+3987
x=1/2