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1.1乘3.2乘100简便计算

1/1×2+1/2×3+1/3×4+……+1/99×100 =1-1/2+1/2-1/3+1/3-1/4+……+1/99-1/100 =1-1/100 =99/100

1*2+2*3+3*4+.....+100*101 =1*(1+1)+2*(2+1)+3*(3+1)+.....+100*(100+1) =1^2+1+2^2+2+3^2+3+...+100^2+100 =(1^2+2^2+3^2+....+100^2)+(1+2+3+....+100) =100(100+1)(2*100+1)/6+(1+100)*100/2 =100*101*201/6+101*100/2 =50*101*67+101*50 =3...

1×2×3×4×5×..........×100 = 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 结果是个158位数,这个叫做100的阶乘

(1十1分之二)乘(1加2分之二)乘(1加上三分2)……乘(1加上100分之二) =(3/1)x(4/2)x(5/3)x(6/4)x(7/5).....x(102/100) =(101x102)/(1x2) =101x51 =5151

1/1*2*3+1/2*3*4+1/3*4*5+……+1/98*99*100 =1/2(2/1*2*3+2/2*3*4+……2/98*99*100) =1/2(1/1*2-1/2*3+1/2*3-1/3*4+……+1/98*99-1/99*100) =1/2(1/1*2-1/99*100) =1/2*4949/9900 =4949/19800

(1+ 1/2)×(1- 1/2)×(1+ 1/3)×(1- 1/3)×...×(1+ 1/99)×(1- 1/99) =(3/2)×(1/2)×(4/3)×(2/3)×...×(100/99)×(98/99) =[(3/2)×(4/3)×...×(100/99)]×[(1/2)×(2/3)×...×(98/99)] =[(3×4×...×100)/(2×3×...×99)]×[(1×2×...×98)/(2×3×...×99)] =(100/2)×...

(1-1/2)(1+1/2)(1-1/3)(1+1/3)...(1-1/100)(1+1/100) =1/2×3/2×2/3×4/3×...×99/100×101/100 =1/2×101/100 =101/200

解:依题意得算式, (1×2)分之1+(2×3)分之1+(3×4)分之1+...+(99×100)分之1 =(1-2分之1)+(2分之1-3分之1)+(3分之1-4分之1)+...+(99分之1-100分之1) =1-2分之1+2分之1-3分之1+3分之1-4分之1+...+99分之1-100分之1 =1-100分之1 =10...

1+100=101 2=99=101 . . . 50+51=101 (1+100)*50=5050 1加到N=(1+N)*N/2(高斯算法) 如果满意记得采纳哦! 你的好评是我前进的动力。 (*^__^*) 嘻嘻…… 我在沙漠中喝着可口可乐,唱着卡拉ok,骑着狮子赶着蚂蚁,手中拿着键盘为你答题!!!

2分之1乘3分之2乘4分之3乘5分之4乘……乘99分之98乘100分之99 =1÷2×2÷3×3÷4×4÷5×……×98÷99×99÷100 =1÷100 =100分之1

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