\(C=\frac{3.8.15....80.99}{4.9.16.81.100}\)

\(=\frac{1.3.2.4.3.5...8.10.9.11}{2.2.3.3.4.4...9.9.10.10}\)

\(=\frac{\left(1.2.3....9\right).\left(3.4.5...10.11\right)}{\left(2.3.4.5...10\right).\left(2.3.4...10\right)}\)

\(=\frac{11}{10}\)

trả lời 

c=\(\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot....\cdot\frac{99}{100}\)

C=\(\frac{3.8.15....99}{4.9.16.100}\)

C=\(\frac{1.3.2.4.3.5.....9.11}{2.2.3.3.4.4....10.10}\)

C=\(\frac{\left(1.2.....9\right)}{2.3....10}.\left(\frac{3.4....11}{2.3...10}\right)\)

C=\(\frac{1}{10}\cdot\frac{11}{2}=\frac{11}{20}\)

làm ẩu quá

đoạn cuối \(=\frac{11}{20}\)nha sorry

bn lê trung hiếu làm đúng rồi !

\(A=\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times\frac{24}{25}\times...\times\frac{899}{900}\)

\(=\frac{1.3}{2.2}\times\frac{2.4}{3.3}\times\frac{3.5}{4.4}\times...\times\frac{29.31}{30.30}\)

\(=\frac{\left(1\times2\times3\times...\times29\right)\left(3\times4\times5\times...\times31\right)}{\left(2\times3\times4\times...\times30\right)\left(2\times3\times4\times...\times30\right)}\)

\(=\frac{1\times2\times3\times...\times29}{2\times3\times4\times...\times30}.\frac{3\times4\times5\times...\times31}{2\times3\times4\times...\times30}\)

\(=\frac{1}{30}.\frac{31}{2}\)

\(=\frac{31}{60}\)

\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}....\frac{899}{900}\\ =\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}....\frac{29.31}{30.30}\\ =\frac{1.2.3.4....29}{2.3.4...30}.\frac{3.4.5...31}{2.3.4...30}\\ =\frac{1}{30}.\frac{31}{2}=\frac{31}{60}\)

.

B = \(\frac{8}{9}.\frac{15}{16}.\frac{24}{25}...\frac{3599}{3600}\)

    = \(\frac{2.4}{3.3}.\frac{3.5}{4.4}.\frac{4.6}{5.5}...\frac{59.61}{60.60}\)

    = \(\frac{2.4.3.5.4.6...59.61}{3.3.4.4.5.5...60.60}\)

    = \(\frac{2.3....59}{3.4...60}.\frac{4.5...61}{3.4...60}\)

    = \(\frac{2}{60}.\frac{61}{3}\)= \(\frac{61}{90}\)

Chúc bạn học tốt!

~ So sad :( !! ~

\(A=\frac{31}{60}\)

I thinks so ! Sad

Hình như sai đề bài bạn nhé! Đề bài đúng như dưới nhé!

\(\frac{3}{4}\).\(\frac{8}{9}.\frac{15}{16}.\frac{24}{25}.\frac{35}{36}.\frac{48}{49}\)

= \(\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.\frac{4.6}{5.5}.\frac{5.7}{6.6}.\frac{6.8}{7.7}\)

= \(\left(\frac{1.2.3.4.5.6}{2.3.4.5.6.7}\right).\left(\frac{3.4.5.6.7.8}{2.3.4.5.6.7}\right)\)

= \(\frac{1}{7}.\frac{8}{2}\)

= \(\frac{1}{7}.4=\frac{4}{7}\)

Hà ơi cho mình hỏi bạn lấy đề ở đâu vậy. Mình lấy đề ở trong sách NĂNG LỰC TỰ HỌC TOÁN 6 đấy.

\(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}...\frac{9999}{10000}=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}....\frac{99.101}{100.100}\)

=\(\frac{1.3.2.4.3.5....999.101}{2.2.3.3.4.4....100.100}=\frac{1.101}{2.100}=\frac{101}{200}\)

a) \(\left(\frac{11}{4}.\frac{-5}{9}-\frac{4}{9}.\frac{11}{4}\right).\frac{8}{33}\)

=\(\frac{11}{4}\left(-\frac{5}{9}-\frac{4}{9}\right).\frac{8}{33}\)

=\(\frac{11}{4}\cdot-1\cdot\frac{8}{33}\)

=\(-\frac{11}{4}\cdot\frac{8}{33}\)

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

b)\(-\frac{1}{4}\cdot\frac{152}{11}+\frac{68}{4}\cdot-\frac{1}{11}\)

=\(\frac{-1.152}{4.11}+\frac{68}{4}\cdot\frac{-1}{11}\)

=\(\frac{-1.152}{11.4}+\frac{68}{4}\cdot\frac{-1}{11}\)

=\(\frac{-1}{11}\cdot\frac{152}{4}+\frac{68}{4}\cdot\frac{-1}{11}\)

=\(\frac{-1}{11}\cdot\left(\frac{152}{4}+\frac{68}{4}\right)\)

=\(\frac{-1}{11}\cdot55=-5\)

c)\(\frac{-2}{3}\cdot\frac{4}{5}+\frac{2}{3}\cdot\frac{3}{5}\)

=\(-1\cdot\frac{2}{3}\left(\frac{4}{5}+\frac{3}{5}\right)\)

=\(-1\cdot\frac{2}{3}\cdot\frac{7}{5}\)

=\(-\frac{2}{3}\cdot\frac{7}{5}\)

=\(\frac{-14}{15}\)

d) chưa nghĩ ra nhé

e) bạn chép sai đề bài rồi

mk mới kiểm tra 45 phút nên biết

đề bài nè

\(\frac{3}{2^2}\cdot\frac{8}{3^2}\cdot\frac{15}{4^2}\cdot...\cdot\frac{899}{30^2}\)

=\(\frac{1.3}{2^2}\cdot\frac{2.4}{3^2}\cdot\frac{3.5}{4^2}\cdot...\cdot\frac{29.31}{30^2}\)

=\(\frac{1.3.2.4.3.5...29.31}{2.2.3^2.4^2...30.30}\)

=\(\frac{1.2.3^2.4^2.5^2....29^2.30.31}{2.2.3^2.4^2.5^2....29^2.30.30}\)

=\(\frac{1.31}{2.30}\)

=\(\frac{31}{60}\)

a)trong ngoac bn dat thau so chung la 11/4 rui tinh binh thuong                                                                         b)bn tu lam nhe                                                                                                                                             c)dat thua so chung                                                                                                                                       d)tinh trong ngoac ra rui nhan vs                                                                                                                       e) mk bo tay 

thanks mấy pn nha

\(B=\frac{8}{9}^.\frac{15}{16}^.\frac{24}{25}^........^.\frac{3599}{3600}\)

\(B=\frac{2.4}{3.3}.\frac{3.5}{4.4}.\frac{4.6}{5.5}.....\frac{59.61}{60.60}\)

B = \(\left(\frac{2.3.4.....59}{3.4.5.....60}\right).\left(\frac{4.5.6.....61}{3.4.5.....60}\right)\)

\(B=\frac{2}{60}.\frac{61}{3}\)

B = \(\frac{61}{90}\)

B= \(\frac{2.4}{3.3}.\frac{3.5}{4.4}.\frac{4.6}{5.5}...\frac{59.61}{60.60}\)

B=\(\frac{2.61}{3.60}\)

B= \(\frac{61}{90}\)