\(B=\dfrac{1}{19}+\dfrac{9}{19.29}+\dfrac{9}{29.39}+...+\dfrac{9}{1999.2009}...">
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21 tháng 5 2017

Lưu An

\(A=\dfrac{1}{19}+\left(\dfrac{9}{19\cdot29}+\dfrac{9}{29\cdot39}+...+\dfrac{9}{1999\cdot2009}\right)\)

\(A=\dfrac{1}{19}+\dfrac{9}{10}\left(\dfrac{10}{19\cdot29}+\dfrac{10}{29\cdot39}+...+\dfrac{10}{1999\cdot2009}\right)\)

\(A=\dfrac{1}{19}+\dfrac{9}{10}\left(\dfrac{1}{19}-\dfrac{1}{29}+\dfrac{1}{29}-\dfrac{1}{39}+...+\dfrac{1}{1999}-\dfrac{1}{2009}\right)\)

\(A=\dfrac{1}{19}+\dfrac{9}{10}\left(\dfrac{1}{19}-\dfrac{1}{2009}\right)\)

\(A=\dfrac{1}{19}+\dfrac{9}{10}\cdot\dfrac{1990}{38171}\)

\(A=\dfrac{1}{19}+\dfrac{1791}{38171}\)

\(A=\dfrac{200}{2009}\)

21 tháng 5 2017

B=1/19+(9/19.29+9/29.39+...+9/1999.2009)

B=1/19+9/10+(10/19.29+10/29.39+.....+10/1999.2009

B=1/19+9/10+(1/19-1/29+1/29-1/39+....+1/1999-1/2009)

B=1/19+9/10+(1/19-1/2009)

B=1/19+9/10.1990/38171

B=1/19+1791/38171

B=200/2009

Vậy B= 200/2009

17 tháng 4 2017

19 tháng 4 2017

Gợi ý: Sử dụng tính chất phân phối của phép nhân đối với phép cộng để nhóm thừa số chung ra ngoài.

Giải bài 76 trang 39 SGK Toán 6 Tập 2 | Giải toán lớp 6

29 tháng 4 2018

c,

= \(\dfrac{5}{9}.\left(\dfrac{7}{13}+\dfrac{9}{13}+\dfrac{-3}{13}\right)\)

= \(\dfrac{5}{9}.1\)

= \(\dfrac{5}{9}\)

29 tháng 4 2018

a,

= \(\dfrac{1}{3}.\left(\dfrac{4}{5}+\dfrac{6}{5}\right)+\dfrac{-4}{3}\)

= \(\dfrac{1}{3}.\dfrac{10}{5}+\dfrac{-4}{3}\)

= \(\dfrac{2}{3}+\dfrac{-4}{3}\)

= \(\dfrac{-2}{3}\)

11 tháng 8 2017

1.

a) \(\dfrac{5}{18}+\dfrac{4}{7}+\dfrac{13}{18}+\dfrac{3}{7}\)

\(=\left(\dfrac{5}{18}+\dfrac{13}{18}\right)+\left(\dfrac{4}{7}+\dfrac{3}{7}\right)\)

\(=1+1=2\)

b) \(\dfrac{4}{9}.\dfrac{5}{19}.\dfrac{9}{4}\)

\(=\left(\dfrac{4}{9}.\dfrac{9}{4}\right).\dfrac{5}{19}\)

\(=1.\dfrac{5}{19}=\dfrac{5}{19}\)

tik mik nha!!!

11 tháng 8 2017

2) \(\dfrac{4}{9}.\dfrac{5}{19}.\dfrac{9}{4} =(\dfrac{4}{9}.\dfrac{9}{4}).\dfrac{5}{19} =1.\dfrac{5}{19} =\dfrac{5}{19}\)

12 tháng 6 2017

\(A=\dfrac{-9}{10^{2010}}+\dfrac{-19}{10^{2011}}=\dfrac{-90}{10^{2011}}+\dfrac{-19}{10^{2011}}=\dfrac{\left(-90\right)+\left(-19\right)}{10^{2011}}=\dfrac{-109}{10^{2011}}\)\(B=\dfrac{-9}{10^{2011}}+\dfrac{-19}{10^{2010}}=\dfrac{-9}{10^{2011}}+\dfrac{-190}{10^{2011}}=\dfrac{\left(-9\right)+\left(-190\right)}{10^{2011}}=\dfrac{-199}{10^{2011}}\)\(\text{Vì }\dfrac{-109}{10^{2011}}>\dfrac{-199}{10^{2011}}\text{ nên }A>B\)

25 tháng 4 2017

\(-2\dfrac{1}{4}.\)\(\left(3\dfrac{5}{12}-1\dfrac{2}{9}\right)\)

=\(\dfrac{-9}{4}\).\(\left(\dfrac{41}{12}-\dfrac{11}{9}\right)\)

=\(\dfrac{-9}{4}.\dfrac{41}{12}-\dfrac{-9}{4}.\dfrac{11}{9}\)

=\(\dfrac{-123}{16}-\dfrac{-11}{4}\)

=\(\dfrac{-123}{16}-\dfrac{-44}{16}\)

=\(\dfrac{-79}{16}\)

25 tháng 4 2017

\(\left(-25\%+0,75+\dfrac{7}{12}\right)\div\left(-2\dfrac{1}{8}\right)\)

=\(\left(\dfrac{-1}{4}+\dfrac{3}{4}+\dfrac{7}{12}\right)\div\left(\dfrac{-17}{8}\right)\)

=\(\left(\dfrac{-3}{12}+\dfrac{9}{12}+\dfrac{7}{12}\right).\dfrac{-8}{17}\)

=\(\dfrac{13}{12}.\dfrac{-8}{17}=\dfrac{-26}{51}\)

28 tháng 3 2017

câu a

\(\left(5\dfrac{7}{9}+2\dfrac{3}{11}\right)-\left(-1\dfrac{8}{11}+3\dfrac{7}{9}\right)\)

= \(5\dfrac{7}{9}+2\dfrac{3}{11}+1\dfrac{8}{11}-3\dfrac{7}{9}\)

= \(\left(5\dfrac{7}{9}-3\dfrac{7}{9}\right)+\left(2\dfrac{3}{11}+1\dfrac{8}{11}\right)\)

= \(2+3\dfrac{11}{11}\)

= \(2+3+1\)

= \(6\)

28 tháng 3 2017

câu b

\(\left(2\dfrac{7}{19}-3\dfrac{8}{9}\right)-\left(1\dfrac{7}{19}-2\dfrac{1}{9}\right)\)

= \(2\dfrac{7}{19}-3\dfrac{8}{9}-1\dfrac{7}{19}+2\dfrac{1}{9}\)

= \(\left(2\dfrac{7}{19}-1\dfrac{7}{19}\right)-\left(3\dfrac{8}{9}-2\dfrac{1}{9}\right)\)

= \(1-1\dfrac{7}{9}\)

= \(\dfrac{-7}{9}\)

6 tháng 4 2017

\(A=15.\left(\dfrac{3}{5}-\dfrac{2}{3}\right)+1\\ A=15.\left(\dfrac{9}{15}-\dfrac{10}{15}\right)+1\\ A=15.\dfrac{-1}{15}+1\\ A=-1+1\\ A=0\)

6 tháng 4 2017

\(C=\dfrac{-5}{7}.\dfrac{2}{11}+\dfrac{-5}{7}.\dfrac{9}{11}+1\dfrac{5}{7}\\ C=\dfrac{-5}{7}.\dfrac{2}{11}+\dfrac{-5}{9}.\dfrac{9}{11}+\dfrac{12}{7}\\ C=\dfrac{-5}{7}.\left(\dfrac{2}{11}+\dfrac{9}{11}\right)+\dfrac{12}{7}\\ C=\dfrac{-5}{7}.1+\dfrac{12}{7}\\ C=\dfrac{-5}{7}+\dfrac{12}{7}\\ C=1\)

6 tháng 3 2018

\(\left(a\right):P=\dfrac{3}{4}.\dfrac{8}{9}.\dfrac{15}{16}....\dfrac{99}{100}\)

Nhận xét

thừa số tổng quát là \(\dfrac{n\left(n+2\right)}{\left(n+1\right)^2}\) với n =1 đến 10

\(P=\dfrac{1.3.2.4.3.5...9.11}{2^2.3^2...9^2.10^2}=\dfrac{\left(1.2.3...9\right)\left(3.4.5....11\right)}{\left(2.3.4....10\right)\left(2.3.4....10\right)}\)

\(P=\dfrac{1.2.3..9}{2.3.4..9.10}.\dfrac{3.4.5...10.11}{2.3.4....10}=\dfrac{1}{10}.\dfrac{11}{2}=\dfrac{11}{20}\)

7 tháng 3 2018

Thanks ak!

4 tháng 4 2017

\(C=\dfrac{6}{7}+\dfrac{5}{8}:5-\dfrac{3}{16}.\left(-2^2\right)\\ C=\dfrac{6}{7}+\dfrac{5}{8}.\dfrac{1}{5}-\dfrac{3}{16}.\left(-4\right)\\ C=\dfrac{6}{7}+\dfrac{1}{8}-\dfrac{3}{16}.\left(-4\right)\\ C=\dfrac{6}{7}+\dfrac{1}{8}-\dfrac{3}{16}.\dfrac{-4}{1}\\ C=\dfrac{6}{7}+\dfrac{1}{8}-\dfrac{-3}{4}\\ C=\dfrac{48}{56}+\dfrac{7}{56}-\dfrac{-42}{56}\\ C=\dfrac{97}{56}\)

4 tháng 4 2017

\(A=15.\left(\dfrac{3}{5}-\dfrac{2}{3}\right)+1\)

\(A=15.\dfrac{-1}{15}+1\)

\(A=-1+1\)

\(A=0\)