\(\dfrac{1}{10}+\dfrac{2}{10}+\dfrac{3}{10}+\dfrac{4}{10}+\dfrac{5}{10}+\) \(\dfrac{6}{10}+\dfrac{7}{10}+\dfrac{8}{10}+\dfrac{9}{10}\)

\(=\dfrac{1+2+3+4+5+6+7+8+9}{10}\)

\(=\dfrac{45}{10}=\dfrac{9}{2}\)

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9/10 = 44/10 = 22/5

bằng 9/2 nhé

Đặt A = \(\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\)

Nhân cả hai với 2 ta được :

2A = \(2\left(\frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\right)\)

=> 2A = \(1+\frac{1}{2^1}+\frac{1}{2^2}+...+\frac{1}{2^9}\)

Trừ 2A cho A , ta được :

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

=> A = \(1-\frac{1}{2^{10}}\)

A=1/2+1/2^2+1/2^3+.............+1/2^10

2A=1+1/2+1/2^2+.............+1/2^9

2a-a=(1/2+1/2^2+1/2^3.....+1/2^10)-(1+1/2+1/2^2............+1/2^9)

=>a=1-1/2^10

=>a=1-1/1024

=>A=1023/1024

\(1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+....+\frac{1}{20}.\left(1+2+....+20\right)\)

\(=1+\frac{1}{2}\times\frac{2.3}{2}+\frac{1}{3}\times\frac{3.4}{2}+...+\frac{1}{20}\times\frac{20.21}{2}\)

\(=\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+...+\frac{21}{2}\)

\(=\frac{\left(2+21\right).20:2}{2}=\frac{230}{2}=115\)

Số cuối là

\(\frac{1}{10}.\left(1+2+3+...+10\right)\) hay \(\frac{1}{20}.\left(1+2+3+...+20\right)\) ??

10 - 9 + 8 - 7 + 6 - 5 + 4 - 3 + 2 - 1

= (10 - 9) + (8 - 7) + (6 - 5) + (4 - 3) + (2 - 1)   

= 1 + 1 + 1 + 1+ 1 = 5

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

\(=\frac{1}{3}+\frac{1}{6}+...+\frac{1}{55}\)

\(=2\left(\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}\right)\)

\(=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\right)=2.\left(\frac{1}{2}-\frac{1}{11}\right)=2.\frac{9}{22}=\frac{9}{11}\)

Số số hạng là :

(50-1):1+1=50(số)

Tổng dãy số là

(50+1)x50:2=1275

Đ/S:1275

k đúng cho m nha

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 +...+ 50

= 1 + 50 + 2 + 49 + 3 + 48 + 4 + 47 + ... + 25 + 26

= (1 + 50) + (2 + 49) + (3 + 48) + (4 + 47) + ... + (25 + 26)

= 51 + 51 + 51 + 51 + ... + 51 (25 số hạng 51 vì 50 : 2 = 25)

= 51 x 25

= 1275

Dãy trên có số số hạng là :

( 50 - 1 ) : 1 + 1 = 50 ( số )

Tổng là :

( 50 + 1 ) x 50 : 2 = 1275

Đáp số : 1275

12

happy new year

12

happy new year

=12 

k minh di lay ban do