Calculate 1 / 1 by 2 + 1 / 2 by 3 +. + 1 / 49 by 50

Calculate 1 / 1 by 2 + 1 / 2 by 3 +. + 1 / 49 by 50

simple form
=1-1/2+1/2-1/3+...+1/49-1/50
=1-1/50
=49/50

One fifty minus one multiplied by one forty-nine minus one multiplied by one forty-eight minus one One third minus one multiplied by one half minus one

The original formula = (- 49 / 50) * (- 48 / 49) * (- 47 / 48) （-2/3)*(-1/2)
=(-1)^49*(1/50)
=-1/50

One minus 50 times one minus 49 times one minus 48 One minus one quarter times one minus one third

(1-1/50)×(1-1/49)×(1-1/48)×...×(1-1/4)×(1-1/3)
=49/50×48/49×47/48×...×3/4×2/3
=2/50
=1/25

What is 49 times 47 out of 48 minus 46? (with a simple algorithm)

(47 / 48 = 46 / 48)
49×（47/48）-46
=（48+1）×（47/48）-46
=48×（47/48）+1×（47/48）-46
=47+（47/48）-46
=1 and 47 / 48

4200 times 51 divided by 17
Hurry up!

4200/50+4200/1+17

99 × 51 simple algorithm

=51*（100-1）
=51*100-51
=5100-51=5049

A simple algorithm of 72 × (51 △ 12)

72×(51÷12)=72÷12×51=6×51=306

Simple algorithm of 46 * 6 + 51 * 4

46*6+46*4 + 5*4 = 46*10 +20 = 480

() / "= 17.51, the minimum can be filled in ()
() / "= 17.51, the minimum can be filled in（

() / "= 17.51, the minimum can be filled in (52)
Because the divisor is bigger than the remainder

3 by 1 / 5 + 5 by 1 / 7 + 7 by 1 / 9 + ······ + 17 by 1 / 19

3 by 1 / 5 + 5 by 1 / 7 + 7 by 1 / 9 + ······ + 17 by 1 / 19
=(1/3-1/5)*1/2+(1/5-1/7)*1/2+…… +（1/17-1/19）*1/2
=（1/3-1/5+1/5-1/7+…… +1/17-1/19）*1/2
=（1/3-1/19）*1/2
=8/57