Đáp án:

Giải thích các bước giải:

8, 3/10+ 3/40+...+ 3/340

= 3/2.5+ 3/5.8+....+3/17.20

= 1/2- 1/5+ 1/5- 1/8+...+ 1/17- 1/20

= 1/2- 1/20

= 9/20

9, $\frac{9}{20}$+ $\frac{3^2}{40}$ +....+ $\frac{3^2}{340}$ 

= 3.( 3/2.5+ 3/5.8+....+3/17.20)

= 3.( 1/2- 1/5+ 1/5- 1/8+...+ 1/17- 1/20)

= 3.( 1/2- 1/20)

= 3.9/20

= 27/20

10, A= 5^2/1.6+ 5^2/6.11+...+ 5^2/26.31

= 5.( 5/1.6+ 5/6.11+..+ 5/26.31)

= 5.( 1- 1/6+ 1/6- 1/11+....+ 1/26- 1/31)

= 5.( 1- 1/31)

=5.30/31

= 150/31

11, 6/15+ 6/35+ 6/63+ 6/99

= 6/3.5+ 6/5.7+6/7.9+ 6/9.11

= 3.( 2/3.5+ 2/5.7+ 2/7.9+ 2/9.11)

= 3.( 1/3- 1/5+ 1/5- 1/6+ 1/6- 1/7+ 1/7- 1/9+ 1/9- 1/11)

= 3.(1/3- 1/11)

=3. 8/33

= 8/11

12, 3/3.5+ 3/5.7+....+ 3/49.51

= 3/2.( 2/3.5+ 2/5.7+....+ 2/49.51)

= 3/2.( 1/3- 1/5+ 1/5- 1/7+....+ 1/49- 1/51)

= 3/2. ( 1/3- 1/51)

= 3/2.16/51

= 8/17

13,A= 1/2+ 2/2.4+ 3/4.7+ 4/7.11+5/11.16

A= 1/1.2+ 2/2.4+ 3/4.7+ 4/7.11+5/11.16

= 1- 1/2+ 1/2- 1/4+...+ 1/11- 1/16

= 1- 1/16

= 15/16

14, A= 1/2+ 2/8+ 3/28+ 4/77+ 5/176

Bạn tách giống câu 13 thôi

= 1/2+ 2/2.4+ 3/4.7+ 4/7.11+5/11.16
A= 1/1.2+ 2/2.4+ 3/4.7+ 4/7.11+5/11.16
= 1- 1/2+ 1/2- 1/4+...+ 1/11- 1/16
= 1- 1/16
= 15/16

Chúc bạn học tốt!