a) \(A=\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+......+\frac{1}{2017.2022}\)

\(5A=5.\left(\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+.....+\frac{1}{2017.2022}\right)\)

\(5A=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+......+\frac{5}{2017.2022}\)

\(5A=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+........+\frac{1}{2017}-\frac{1}{2022}\)

\(5A=1-\frac{1}{2022}\)

\(5A=\frac{2022}{2022}-\frac{1}{2022}\)

\(5A=\frac{2021}{2022}\)

\(A=\frac{2021}{2022}\div5\)

\(A=\frac{20201}{10110}\)

TL: 

\(\frac{5}{6}=\frac{1}{2}+\frac{1}{3}\) 

@@@@@@@@@@ 

HT

Gọi A=1/1x6+1/6x11+1/11x16+...+1/96x101

A=1/1x6+1/6x11+1/11x16+...+1/96x101

5A=5/1x6+5/6x11+5/11x16+...+5/96x101

5A=1-1/6+1/6-1/11+1/11-1/16+...+1/96-1/101

5A=1-1/101

5A=100/101

A=100/101:5

A=20/101.

Nếu đúng thì kết bạn với mình nhé.Mình học lớp 6C của trường THCS An Khê.Tên Đỗ Đường Hùng.

= 1/5 . (5/1.6 + 5/6.11 + ...... + 5/96.101)

= 1/5 . (1-1/6+1/6-1/11+.....+1/96-1/101)

= 1/5.(1-1/101)

= 1/5 . 100/101

= 20/101

Tk mk nha

=1/1-1/6+1/6-1/11+1/11-1/16+...+1/96-1/101                                                                                                                                                      =1-1/101=100/101    

Bằng \(-0,4041667168\)

A=2/1.3 + 2/3.5 + 2/5.7 + ... + 2/99.101

A= 2 - 1/3 + 1/3 - 1/5 + 1/5 - ... + 2/99 - 2/101

A = 2 - 2/101 = 200/101

B = 3-1/3+1/3-1/5+1/5-...+3/49-3/51

B = 3-3/51(tự tính nhé)

C = 5(5/1.6+5/6.11+5/11.16+....+5/26-5/31

C = 5(5-1/31)(tự tính)

D rút gon cho 2 rồi 3D , sau đó 5(3/.... tương tự các cách làm trên)

2E nhân lên rồi giải giống trên

3F Rồi nhân 4/77 và rút gọn thì tính được

a, A= \(\frac{1}{1}\)- \(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{5}\)+......+\(\frac{1}{99}\)-\(\frac{1}{100}\)

A=\(\frac{1}{1}\)-\(\frac{1}{100}\)+(-\(\frac{1}{3}\)+\(\frac{1}{3}\)-.....-\(\frac{1}{99}\)+\(\frac{1}{99}\))

A=\(\frac{1}{1}\)-\(\frac{1}{100}\)+0

A=1-\(\frac{1}{100}\)=\(\frac{100}{100}\)-\(\frac{1}{100}\)=\(\frac{99}{100}\)

a) A= \(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{99.101}\) 

=\(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)

=\(1-\frac{1}{100}=\frac{99}{100}\)

b) \(\frac{3}{1.3}+\frac{3}{3.5}+...+\frac{3}{49.51}\)

=\(\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{49.51}\right).\frac{3}{2}\)

=\(\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{49}-\frac{1}{50}\right).\frac{3}{2}\)

= \(\left(1-\frac{1}{50}\right).\frac{3}{2}=\frac{49}{50}.\frac{3}{2}=\frac{147}{100}\)

c) \(C=\frac{5^2}{1.6}+\frac{5^2}{6.11}+...+\frac{5^2}{26.31}\)

= \(\left(\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{26.31}\right).5\)

= \(\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{26}-\frac{1}{31}\right).5\) 

= \(\left(1-\frac{1}{31}\right).5=\frac{30}{31}.5=\frac{150}{31}\)

Mấy bài còn lại mik đang phải nháp đã. Bạn thông cảm cho mik

\(A=\frac{5\cdot5}{1.6}+\frac{5.5}{6.11}+...+\frac{5.5}{26.31}\)

\(=5\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{26}-\frac{1}{31}\right)\)

\(=5\left(1-\frac{1}{31}\right)\)

\(=5\times\frac{30}{31}\)

\(=\frac{150}{31}\)

đề sai

\(\frac{2619}{48520}\)

a,=1/2-1/5+1/5-1/8+1/8-1/11+...+1/17-1/20

    =1/2-1/20=19/20

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

    =5.(1-1/31)=5.30/31 =150/31

\(\frac{5^2.3^{11}.2^{11}.2^8+2^2.3^2.3^2.5^2}{2.2^{12}.3^{12}.2^4.5^4-3^8.2^{18}.3^3.5^3}\)

\(=\frac{5^2.3^{11}.2^{19}+2^2.3^4.5^2}{2^{17}.3^{12}.5^4-3^{11}.2^{18}.5^3}\)

\(=\frac{5^2.3^4.2^2.\left(3^7.2^{17}+1\right)}{2^{17}.3^{11}.5^3.\left(3.5-2\right)}=\frac{3^7.2^{17}}{2^{15}.3^7.5}+\frac{1}{2^{15}.3^7.5}=\frac{4}{5}+\frac{1}{2^{15}.3^7.5}\)