\(B=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{9900}\)

\(B=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\)

\(B=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)

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

\(B=\frac{99}{100}\)

\(B=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{9900}\) 

  \(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\)

  \(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)

  \(=1+\left(-\frac{1}{2}+\frac{1}{2}\right)+\left(-\frac{1}{3}+\frac{1}{3}\right)+\left(-\frac{1}{4}+\frac{1}{4}\right)+...+\left(-\frac{1}{99}+\frac{1}{99}\right)-\frac{1}{100}\)

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

1-1/2+1/2-1/3+1/3+1/4-1/4+1/5-1/5+1/6-1/6+1/7-1/7+1/8-1/8+1/9-1/9+1/10-(1-1/3+1/3-3/5+3/5-4/7+5/9-5/9+6/11-6/11-7/13)=1+1/10-1+7/13=83/130

A=(5/9+4/9)-(7/8+1/8)+(2/3+1/3)

1-1+1=1

release

tỷtyryryyr

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

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

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

b) \(B=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)

=> \(B=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)

=> \(B=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)

=> \(B=\frac{1}{1}-\frac{1}{7}=\frac{6}{7}\)

a, A = 5/11x16 + 5/16x21 + 5/21x26 + ... + 5/61x66

       = (5/11 - 5/16) + (5/16 - 5/21) + (5/21 - 5/26) + ... + (5/61 - 5/66)

       = 5/11 - 5/66 ( phá ngoặc rồi nhóm biểu thức trên)

       = 25/66

b, B = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42

       = 1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 + 1/6x7

       = (1/1 - 1/2) + (1/2-1/3) + (1/3 - 1/4) + (1/4 - 1/5) + ( 1/5 -1/6) + (1/6 - 1/7)

       = 1/1 - 1/7 = 6/7

c, C = 7/3x4x5 + 7/4x5x6 + 7/5x6x7 +... + 7/19x20x21

   C =7/2 x ( 2/3x4x5 + 2/4x5x6 + ... + 2/19x20x21)

   C = 7/2 x [(1/3-1/4-1/5) + (1/4-1/5-1/6) + ...+(1/19-1/20-1/21)]

   C = 7/2 x (1/3 - 1/21) (cũng phá ngoặc rồi nhóm như các câu trên)

   C = 1

Dễ nhưng dài quá !

ngu te rua ma khong biet

a,

= 44.(82+18)-4oo

= 44.100-400

= 4400-400

= 4000 

b,

= [319+(-219)]+[598+(-98)

=100+500

=600

c,

= (17/28+18/29-19/30-20/31).0

=0

k cho mik nhé

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

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

\(=\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{20.21}\)

\(=2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{20.21}\right)\)

\(=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{20}-\frac{1}{21}\right)\)

\(=2\left(1-\frac{1}{21}\right)=2.\frac{20}{21}=\frac{40}{21}\)

mk lại làm thế này 

A= 1/3 +1/6 +1/10 +.....+1/210

A= 1/1*3 +1/3*2 +1/5*2 +...... +1/5*42

A : 2 = 1/6 +1/12 +1/20 +... +1/420

A : 2  = 1/2*3 +1/3*4 +1/4*5 +....+ 1/10*42

A ;2= 1/2 -1/3 +1/3 -1/4 +1/4 -1/5 +.....+1/10 -1/42

A: 2 = 1/2  - 1/42 = 11/21

A= 10/21 * 2 

A= 20/21

thế đấy mk lại làm khác bn