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Đặt : \(A=10.11+11.12+...+98.99+99.100\)

\(\Rightarrow3A=10.11.3+11.12.3+...+98.99.3+99.100.3\)

\(\Rightarrow3A=10.11.\left(12-9\right)+11.12.\left(13-10\right)+...+\)\(98.99.\left(100-97\right)+99.100.\left(101-98\right)\)

10.11+11.12+12.13+...+97.98+98.99+99.100

=10-11+11-12+12-13+...+97-98+98-99+99-100

=10-100

=-90

Đặt A = 10.11 + 11.12 + ... + 98.99 + 99.100 

3A = 10.11.3 + 11.12.3 + ... + 98.99.3 + 99.100.3 

3A = 10.11.(12 -9) + 11.12.(13-10) + ... + 98.99.(100 - 97) + 99.100.(101-98)

3A = 10.11.12 - 9.10.11 + 11.12.13 - 10.11.12 + ... + 98.99.100 - 97.98.99 + 99.100.101 - 98.99.100 

3A = (10.11.12 + 11.12.13 + ... + 98.99.100 + 99.100.101) - (9.10.11 + 10.11.12 + ... + 97.98.99 + 98.99.100)

3A = 99.100.101 - 9.10.11 

3A = 999799 

A = 999799 : 3  

giúp tớ với

Số số hạng là(99,100-10,11):0,01+1=8900

=>Tổng=8900:2x(10,11+99,100)=485984,5

\(\dfrac{3}{10.11}\) + \(\dfrac{3}{11.12}\) + \(\dfrac{3}{12.13}\) + \(\dfrac{3}{13.14}\) + \(\dfrac{3}{14.15}\)

= \(\dfrac{3}{10}\) - \(\dfrac{3}{11}\) + \(\dfrac{3}{11}\) - \(\dfrac{3}{12}\) + \(\dfrac{3}{12}\) - \(\dfrac{3}{13}\) + \(\dfrac{3}{13}\) - \(\dfrac{3}{14}\) + \(\dfrac{3}{14}\) - \(\dfrac{3}{15}\)

= \(\dfrac{3}{10}\) - \(\dfrac{3}{15}\) = \(\dfrac{1}{10}\)

\(\dfrac{3}{10.11}+\dfrac{3}{11.12}+\dfrac{3}{12.13}+\dfrac{3}{13.14}+\dfrac{3}{14.15}\)

\(=\dfrac{3}{1}.\left(\dfrac{3}{10}-\dfrac{3}{11}+\dfrac{3}{11}-\dfrac{3}{12}+\dfrac{3}{12}-\dfrac{3}{13}+\dfrac{3}{13}-\dfrac{3}{14}+\dfrac{3}{14}-\dfrac{3}{15}\right)\)

\(=\dfrac{3}{1}.\left(\dfrac{3}{10}-\dfrac{3}{15}\right)\)

\(=\dfrac{3}{1}.\left(\dfrac{9}{30}-\dfrac{6}{30}\right)\)

\(=\dfrac{3}{1}.\dfrac{1}{10}\)

\(=\dfrac{3}{10}\)

A= 5/10.11+5/11.12+5/12.13+5/13.14+5/14.15

A= (1/10.11+1/11.12+1/12.13+1/13.14+1/14.15) :5

A= [(1/10-1/11)+(1/11-1/12)+(1/12-1/13)+(1/13-1/14)+(1/14-1/15)] :5

A= (1/10-1/15):5

A= 1/30:5

A= 1/150

Ta có A=1/10.11+1/11.12+...+1/98.99+1/99.100

            =1/10-1/11+1/11-1/12+...+1/98-1/99+1/99-1/100

            =1/10-1/100

           =10/100-1/100

          =9/100

Vậy A=9/100

Giải:

A=1/10.11+1/11.12+...+1/98.99+1/99.100

A=1/10-1/11+1/11-1/12+...+1/98-1/99+1/99-1/100

A=1/10-1/100

A=9/100

Chúc bạn học tốt!

=1/10 - 1/11+......+1/99-1/100

=1/10-1/100

=9/100