Question

小学生数学：（1+1/2+1/3+1/4)×(1/3+1/4+1)-(1+1/3+1/4)×(1/2+1/3+1/4)= 求解答

小学生数学：（1+1/2+1/3+1/4)×(1/3+1/4+1)-(1+1/3+1/4)×(1/2+1/3+1/4)= 求解答

Answer 1

答案：41650

一般的，（用*表示相乘）

设S=1*2+2*3+3*4+……n*(n+1)
则3S=1*2*3+2*3*3+3*4*3+4*5*3+……n*(n+1)*3
=1*2(3-0)+2*3(4-1)+3*4(5-2)+……n(n+1)[n+2-(n-1)]
=1*2*3+2*3*4-1*2*3+3*4*5-2*3*4+……+n(n+1)(n+2)-(n-1)n(n+1)
=n(n+1)(n+2)，
所以原式=S=n(n+1)(n+2)/3

故S=49*(49+1)*(49+2)/3=41650

Answer 2

设a=1/3+1/4，则
（1+1/2+1/3+1/4)×(1/3+1/4+1)-(1+1/3+1/4)×(1/2+1/3+1/4)

=（1+1/2+a)×(a+1)-(1+a)×(1/2+a)
=(a+1)+1/2(a+1)+a(a+1)-1/2(a+1)-a(a+1)
=a+1
=1/3+1/4+1
=1又12分之7。

Answer 3

=(1+1/3+1/4)(1+1/2+1/3+1/4-1/2-1/3-1/4)
=(1+1/3+1/4)*1
=1+1/3+1/4
=19/12

Answer 4

(25/12)*(19/12)-(19/12)*(13/12)
=(19/12)*1
=19/12