Giải thích các bước giải:
a,
= 1/3 - 1/7 + 1/7 - 1/11 + 1/11 - 1/15 + 1/15 - 1/19 + 1/19 + 1/23 + 1/23 - 1/27
= 1/3- 1/27
= 8/27
b,
= (1/3 - 1/5 + 1/5 - 1/7 + 1/7- 1/9 + 1/9 - 1/11 + 1/11 - 1/13 - 1/15) + 2 x ( 1 - 1/2 +1/2 - 1/3 + 1/3 - 1/4 + .... + 1/8 - 1/9 + 1/9 - 1/10)
= ( 1/3 - 1/15) + 2 x ( 1 - 1/10 )
= 4/15 + 2 x 9/10
= 4/ 15 + 9/5
= 4/ 15 + 27/15
= 31/15
c,
= 3 x ( 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + ...... + 3/9 - 3/10) + 11x ( 1/2 - 1/9 + 1/9 - 1/16 + 1/16 - 1/23 +........+ 1/93 - 1/100)
= 3 x ( 1- 3/10 ) + 11 x ( 1/9 - 1/100)
= 3 x 7/10 + 11 x 91/100
= 21/10 + 1001/100
= 210/100 + 1001/100
= 1211/1000
d, = 4/3 x ( 1/3 - 1/6 + 1/6 - 1/9 + 1/9 - 1/12 + 1/12 - 1/15)
= 4/3 x ( 1/3 - 1/15 )
= 4/3 x 4/15
= 16/45
đ,
= 7/4 x ( 1 - 1/5 + 1/5 - 1/9 + 1/9 - 1/13 + 1/13 - 1/17 + 1/17 - 1/21 )
= 7/4 x ( 1 - 1/21 )
= 7/4 X 20/21
= 5/3
