有一道小学数学题不会,帮帮忙拉(是一道计算题)
1/4+1/28+1/70+...+1/9700 =1/(1*4)+1/(4*7)+1/(7*10)+...1/(97*100) =1/3(1/1-1/4)+1/3(1/4-1/7)+1/3(1/7-1/10)+...1/3(1/97-1/100) =1/3(1-1/4+1/4-1/7+1/7-1/10+...1/97-1/100) =1/3(1-1/100) =1/3*(99/100) =33/100 公式:1/(a*b) (b>a) =[1/(b-a)] *(1/a-1/b) 意思是:分母为两数乘积分子为1的分数如1/(a*b),可分解为两数中大数b减小数a的差做分母的分子为1的分数1/(b-a),再乘以以小数为分母的分子为1的分数1/a和以大数为分母的分子为1的分数1/b的差(1/a-1/b)
对不起,我也不懂
¼+1/28+1/70+...+1/9700 =1/(1*4)+1/(4*7)+1/(7*10)+...1/(97*100) =1/3(1/1-¼)+1/3(¼-1/7)+1/3(1/7-1/10)+...1/3(1/97-1/100) =1/3(1-¼+¼-1/7+1/7-1/10+...1/97-1/100) =1/3(1-1/100) =1/3*(99/100) =33/100 参考资料:
考点:拆分,这个以后很常用,请记住另外,千万要记住这个 1/3 ,这很关键的!¼+1/28+1/70+...+1/9700 =1/(1*4)+1/(4*7)+1/(7*10)+...1/(97*100) =1/3(1/1-¼)+1/3(¼-1/7)+1/3(1/7-1/10)+...1/3(1/97-1/100) =1/3(1-¼+¼-1/7+1/7-1/10+...1/97-1/100) =1/3(1-1/100) =1/3*(99/100) =33/100
答:详情>>