A= 3/11*16+3/16*21+3/21*26+.....+3/61*66

\(=\frac{3}{5}\left(\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{61.66}\right)\)

\(=\frac{3}{5}\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\right)\)

\(=\frac{3}{5}\left(\frac{1}{11}-\frac{1}{66}\right)\)

\(=\frac{3}{5}\cdot\frac{5}{66}\)

\(=\frac{1}{22}\)

\(A=\frac{3}{11.16}+\frac{3}{16.21}+\frac{3}{21.26}+...+\frac{3}{61.66}\)

\(\Rightarrow A=\frac{3}{5}\left(\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+...+\frac{5}{61.66}\right)\)

\(\Rightarrow A=\frac{3}{5}.\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\right)\)

\(\Rightarrow A=\frac{3}{5}.\left(\frac{1}{11}-\frac{1}{66}\right)\)

\(\Rightarrow A=\frac{3}{5}.\frac{5}{66}\)

\(\Rightarrow A=\frac{1}{22}\)

Vậy \(A=\frac{1}{22}\)

`#3107`

\(A=1+2^1+2^2+2^3+...+2^{2015}\)

\(2A=2+2^2+2^3+2^4+...+2^{2016}\)

\(2A-A=\left(2+2^2+2^3+2^4+...+2^{2016}\right)-\left(1+2+2^2+2^3+...+2^{2015}\right)\)

\(A=2+2^2+2^3+2^4+...+2^{2016}-1-2-2^2-2^3-...-2^{2015}\)

\(A=2^{2016}-1\)

Vậy, \(A=2^{2016}-1.\)

\(A=2^0+2^1+2^2+...+2^{2015}\)

\(2\cdot A=2^1+2^2+2^3+...+2^{2016}\)

\(A=2A-A=2^{2016}-2^0\)

\(A=2^{2016}-1\)

Sửa đề:\(A=4+4^2+4^3+...+4^{21}\)

=>\(4A=4^2+4^3+...+4^{22}\)

=>\(4A-A=4^{22}+4^{21}+...+4^3+4^2-4^{21}-...-4^3-4^2\)

=>\(3A=4^{22}-4^2\)

=>\(A=\dfrac{4^{22}-4^2}{3}\)

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

\(=\left(4+4^2+4^3\right)+\left(4^4+4^5+4^6\right)+...+\left(4^{19}+4^{20}+4^{21}\right)\)

\(=4\left(1+4+4^2\right)+4^4\left(1+4+4^2\right)+...+4^{19}\left(1+4+4^2\right)\)

\(=21\left(4+4^4+...+4^{19}\right)⋮21\)

\(A=\frac{3}{11.16}+\frac{3}{16.21}+\frac{3}{21.26}+...+\frac{3}{61.66}\) 

\(A:3.5=\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+...+\frac{5}{61.66}\)

\(A:3.5=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\)

\(A:3.5=\frac{1}{11}-\frac{1}{66}=\frac{5}{66}\)

=> \(A=\frac{5}{66}:5.3=\frac{1}{22}\)

\(A=\frac{3}{11.16}+\frac{3}{16.21}+\frac{3}{21.26}+...+\frac{3}{61.66}\)

\(A=\frac{3}{5}.\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\right)\)

\(A=\frac{3}{5}.\left(\frac{1}{11}-\frac{1}{66}\right)\)

\(A=\frac{3}{5}.\frac{5}{66}\)

\(A=\frac{15}{330}\)

Rồi nha

Ý cha, nếu bạn An Hòa ra = \(\frac{1}{22}\) thì kết quả cuối cùng của bài mình bạn rút gọn đi nha (\(\frac{15}{330}=\frac{1}{22}\))

Ta co: A = 1/10+ 1/15+1/21+...+1/120 

              = 2/20+2/30+2/42+...+2/240=2/(4*5)+2/(5*6)+.....+2/(15*16)

              = 2*[1/(4*5)+1/(5*6)+...........+ 1/(15*16)]

              = 2* [ 1/4-1/5+1/5-1/6+.........+1/15-1/16]

              = 2*[1/4-1/16]

             = 2*3/16

              = 3/8

Vay A=3/8

C = 2a + 18b + 5b + 21a

C = a ( 21 + 2 ) + b ( 18 + 5 )

C = 23a + 23b

C = 23 ( a + b )

mà a + b = 5 ( đề bài )

=> C = 23 x 5

=> C = 115

Vậy,.........

a) -57.11=-57.(10+1)=-570-57=-627

b) 75.(-21)=-75.21=-75.(20+1)=-1500-75=-1575

k nhé mn!

Phương pháp giải

- Đặt tính : Viết phép tính theo hàng dọc sao cho các chữ số cùng hàng thẳng cột với nhau.

- Tính : Cộng lần lượt các số theo thứ tự từ phải sang trái.

Lời giải chi tiết:

a)

b)

c)