A. Dãy số có số số hạng là

    ( 20/21 - 1/21) :1/21 + 1 = 20

Tổng dãy trên là 

   ( 1/21 + 20/21) x 20 : 2 = 10

B.  3/7 + 4/19 + 7/11 + 15/11 + 15/19 + 4/7

= 4

D

D

D

a) \(\dfrac{-25}{19}< \dfrac{-13}{19}< \dfrac{9}{19}< \dfrac{14}{19}< \dfrac{20}{19}< \dfrac{30}{19}< \dfrac{42}{19}\)

b) \(\dfrac{-2}{15}< \dfrac{-1}{10}< \dfrac{1}{6}< \dfrac{1}{5}< \dfrac{4}{15}< \dfrac{1}{3}< \dfrac{2}{5}\)

Tính nhẩm rồi điền kết quả vào chỗ trống.

14 - 1 = 13     15 - 4 = 11     17 - 2 = 15     15 - 3 = 12

15 - 1 = 14     19 - 8 = 11     16 - 2 = 14     15 - 2 = 13

1)C= 1/5+1/10+1/20+1/40+...+1/1280

\(=\frac{1}{5}\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^8}\right)\)

Đặt cái trong ngoặc là A ta có:\(2A=2+1+...+\frac{1}{2^7}\)

\(2A-A=\left(2+1+...+\frac{1}{2^7}\right)-\left(1+\frac{1}{2}+...+\frac{1}{2^8}\right)\)

\(A=2-\frac{1}{2^8}\).Thay A vào ta được:\(C=\frac{1}{5}\left(2-\frac{1}{2^8}\right)=\frac{1}{5}\cdot\frac{511}{256}=\frac{511}{1280}\)

2)D= 2/1*3+2/3*5+2/5*10+2/7*9+2/9*11+2/11*18+2/13*15

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{13}-\frac{1}{15}\)

\(=1-\frac{1}{15}\)

\(=\frac{14}{15}\)

3)E= 4/3*7+4/7*11+4/11*15+4/15*19+4/19*23+4/23*27

\(=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{23}-\frac{1}{27}\)

\(=\frac{1}{3}-\frac{1}{27}\)

\(=\frac{8}{27}\)

4)G= 1/2+1/6+1/12+1/20+1/30+1/42+...+1/110

\(=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{10.11}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{10}-\frac{1}{11}\)

\(=1-\frac{1}{11}\)

\(=\frac{10}{11}\)

5)H= 3/1*2+3/2*3+3/3*4+3/4*5+...+3/9*10

\(=3\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\right)\)

\(=3\left(1-\frac{1}{10}\right)\)

\(=3\times\frac{9}{10}\)

\(=\frac{27}{10}\).Lần sau bạn đăng ít một thôi nhé 

14) \(\sqrt{7-4\sqrt{3}}=2-\sqrt{3}\)

15) \(\sqrt{8+2\sqrt{15}}=\sqrt{5}+\sqrt{3}\)

16) \(\sqrt{10-2\sqrt{21}}=\sqrt{7}-\sqrt{3}\)

17) \(\sqrt{11+2\sqrt{18}}=3+\sqrt{2}\)

18) \(\sqrt{7+2\sqrt{10}}=\sqrt{5}+\sqrt{2}\)

19) \(\sqrt{7+4\sqrt{3}}=2+\sqrt{3}\)

20) \(\sqrt{12-2\sqrt{35}}=\sqrt{7}-\sqrt{5}\)

\(\sqrt{7-4\sqrt{3}}=\sqrt{2^2-2.2.\sqrt{3}+\left(\sqrt{3}\right)^2}=\sqrt{\left(2-\sqrt{3}\right)^2}=\left|2-\sqrt{3}\right|=2-\sqrt{3}\)

√7−4√3=√22−2.2.√3+(√3)2=√(2−√3)2=∣∣2−√3∣∣=2−√3

1+2+3+4+5+...+15+16+17+18+19+20

= ( 1 + 19 ) + ( 2 + 18 ) + ( 3 + 17 ) + ( 4 + 16 ) + ( 5 + 15 ) + ... + ( 9 + 11 ) +  ( 10 + 20 )

= 20 + 20 + 20 + 20 + ... + 20 + 30

= 180 + 30 = 210

Tính số phần tử:   \(\text{1+2+3+4+...+18+19+20}\) 
                              \(=\left(20-1\right):1+1\) \(=20\)

Tổng : \(\dfrac{\left(20+1\right)\times20}{2}=210\)

10 < 10 + 3

11 + 2=2 + 11

9 < 10 + 9

10 = 10 + 0

17 – 4 > 14 - 3

18 – 4 >12

15 > 15 – 1

17 + 1<17 + 2

12+ 5 > 16

16 =19 - 3

15 – 4 =10 + 1

19 – 3 >11

20-19+18-17+16-15+14-13+12-11+11-10+10-9+9-8+8-7+7-6+6-5+5-4+4-3+3-2+2-1

=1+1+1+1+1+1+1+1+1+1+1+1+1+1+1

=1x15

=15

tk nhé

20 - 19 + 18 - 17 + 16 - 15 + ... + 4 - 3 + 2 - 1

= ( 20 - 19 ) + ( 18 - 17 ) + ( 16 - 15 ) + ... + ( 4 - 3 ) + ( 2 - 1 )

=> Có 10 cặp số 1

<=> 1 x 10 

= 10

Đáp số: Kết quả là 10 

15