Question

Bài 5 : Tính nhanh :                                                                                                                                                                                   \(\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}+\frac{55}{56}+\frac{71}{72}\)

Answer 1

=[1-1/2]+[1-1/6]+[1-1/12]+...+[1-1/56]+[1-1/72]

=8*1-[1/2+1/6+1/12+...+1/56+1/72]

=8-[1/1*2+1/2*3+1/3*4+...+1/7*8+1/8*9]

=8-[1/1-1/2+1/2-1/3+1/3-1/4+...+1/7-1/8+1/8-1/9]

=8-[1-1/9]

=8-8/9

=7/1/9

 

Answer 2

= (1- 1/2) + (1- 5/6) + (1- 11/12) + ( 1- 19/20) + (1- 29/30) + (1- 41/42) + (1- 55/56) + (1-71/72)

= 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72

= 8 - ( 1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9)

= 8                    -          8/9

= 64/9

Answer 3

= 64/9 nha em