Bài 10:
d, 989898/454545 - 31313131/15151515
= 10101.98/10101.45 - 1010101.31/1010101.15
= 98/45 - 31/15
= 98/45 - 93/45
= 2/45

Bài 2
Gọi số hạng cuối cung của dãy S là 4/(x-4)x
=> S = 4/3.7 + 4/7.11 + 4/11.15 +...+ 4/(x-4)x = 664/1995
        = 1/3 - 1/7 + 1/7 - 1/11 + 1/11 - 1/15 + ...+ 1/(x-4) - 1/x = 664/1995
        = 1/3 - 1/x = 664/1995
        = (x-3)/3x = 664/1995
        = 1995(x-3) = 3x.664
Có 1995(x-3) = 3x.664
=> 1995x - 5985 = 1992x
=> 1995x - 1992x = 5985
=> 3x = 5985
=> x = 1995
Số hạng cuối của dãy S là : 4/(1995-4).1995 = 4/1991.1995
        

1
a, 4/3x7 + 4/7x11 + 4/11x15 + ... + 4/19x23 + 4/23x27
= 1/3 - 1/7 + 1/7 - 1/11+1/11 - 1/15 +...+ 1/19 - 1/23 + 1/23 - 1/27
= 1/3 - 1/27
= 8/27
b, 2/3x5 + 2/5x7 + 2/7x9 + ... + 2/13x15
= 1/3 - 1/5 + 1/5 - 1/7 +1/7 - 1/9 + ... + 1/13 - 1/15
= 1/3 - 1/15 = 4/15
c, 3/1x2 + 3/2x3 + 3/3x4 + ...+ 3/9x10 + 77/2x9 + 77/9x16 + ... + 77/93x100
= 3x(1/1-1/2 + 1/2 - 1/3 +1/3 - 1/4 + ... + 1/9 - 1/10 ) + 11 x (1/2 - 1/9 + 1/9 -1/16 + 1/16 - 1/23 + ... + 1/93 - 1/100)
= 3x (1 - 1/10) + 11 x(1/2 - 1/100)
= 3x 9/10 + 11x 49/100
= 27/10 + 539/100 = 809/100
d , 4/3x6 + 4/6x9 + 4/9x12 + 4/12x15
= 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, 7/1x5 + 7/5x9 + ... + 7/17x21
= 7/4 x ( 1/1 - 1/5 + 1/5 -1/9 + ...+ 1/17 - 1/21 )
= 7/4 x ( 1 - 1/21 )
= 7/4 x 20/21
= 5 /3
e, 1/2 + 1/6 + 1/12 + ...+ 1/110
= 1/1x2 + 1/2x3 + 1/3x4 + ... + 1/10x11
=1 - 1/2 + 1/2 - 1/3 + 1/3 -1/4 + 1/4 -1/5 + ... + 1/10 -1/11
= 1 - 1/11
= 10/11
g, 1/10 + 1/40 + 1/88 + 1/154 +1/238 + 1/340
= 1/2x5 + 1/5x8 + 1/8x11 + 1/11x14 + 1/14x17 + 1/17x20
= 1/3 x ( 1/2 - 1/5 + 1/5 - 1/8 +1/8 - 1/11 + 1/11 - 1/ 14 + 1/14 - 1/17 + 1/17 - 1/20)
= 1/3 x (1/2 - 1/20)
= 1/3 x 9/20
= 3/20