tính A=\(\left(1+\frac{7}{9}\right)\left(1+\frac{7}{20}\right)\left(1+\frac{7}{33}\right)\left(1+\frac{7}{48}\right)......\left(1+\frac{7}{2009}\right)\)
Tính
a) \(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{2018}\right)\)
b) \(\left(1-\frac{1}{3}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{10}\right)\left(1-\frac{1}{15}\right)...\left(1-\frac{1}{190}\right)\)
c) \(\left(1+\frac{7}{9}\right)\left(1+\frac{7}{20}\right)\left(1+\frac{7}{33}\right)\left(1+\frac{7}{48}\right)...\left(1+\frac{7}{2009}\right)\)
a) =\(\frac{1}{2}.\frac{2}{3}.....\frac{2017}{2018}=\frac{1.2.....2017}{2.3.4.....2018}=\frac{1}{2018}\)
Tính
a) \(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{2018}\right)\)
b) \(\left(1-\frac{1}{3}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{10}\right)\left(1-\frac{1}{15}\right)...\left(1-\frac{1}{190}\right)\)
c) \(\left(1+\frac{7}{9}\right)\left(1+\frac{7}{20}\right)\left(1+\frac{7}{33}\right)\left(1+\frac{7}{48}\right)...\left(1+\frac{7}{2009}\right)\)
a) \(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{2018}\right)\)
\(=\frac{1}{2}.\frac{2}{3}...\frac{2017}{2018}\)
\(=\frac{1.2...2017}{2.3...2018}\)
\(=\frac{1}{2018}\)
b) \(\left(1-\frac{1}{3}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{10}\right)\left(1-\frac{1}{15}\right)...\left(1-\frac{1}{190}\right)\)
\(=\frac{2}{3}.\frac{5}{6}.\frac{9}{10}.\frac{14}{15}...\frac{189}{190}\)
\(=\frac{4}{6}.\frac{10}{12}.\frac{18}{20}.\frac{28}{30}...\frac{378}{380}\)
\(=\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}.\frac{7.4}{5.6}...\frac{18.21}{19.20}\)
\(=\frac{\left(1.2.3...18\right).\left(4.5.6...21\right)}{\left(2.3.4...19\right).\left(3.4.5...20\right)}\)
\(=\frac{1.21}{19.3}\)
\(=\frac{21}{57}\)
c) \(\left(1+\frac{7}{9}\right)\left(1+\frac{7}{20}\right)\left(1+\frac{7}{33}\right)\left(1+\frac{7}{48}\right)...\left(1+\frac{7}{2009}\right)\)
\(=\frac{16}{9}.\frac{27}{20}.\frac{40}{33}.\frac{56}{48}...\frac{2016}{2009}\)
mk ko bít làm câu c ! xin lỗi bn nha! bn tự nghĩ cách làm câu c giúp mk nhé!
Tính:
\(\left(1+\frac{7}{9}\right)\times\left(1+\frac{7}{20}\right)\times\left(1+\frac{7}{33}\right)\times\left(1+\frac{7}{48}\right)\times....\times\left(1+\frac{7}{180}\right)\)
Thần đòng nào giỏi toán vào giúp mik zới!Chiều nay thi rồi huhu!!!!!!!!!
(1+7/9).(1+7/20).(1+7/33).(1+7/48)......(1+7/180)
=16/9.27/20.40/33.55/48........187/180
=2.8/1.9 . 3.9/2.10 . 4.10/3.11 . 5.11/4.12 ........ 11.17/18.10
=(2.3.4.5.......11).(8.9.10......17)/(1.2.3.4.....18).(9.10.11.12......18)
=11.8/1.18=88/18=44/9
Ta có: (1 + 7/9) x (1 + 7/20) x (1 + 7/33) x (1 + 7/48) x ...x (1 + 7/180)
= (9/9 + 7/9) x (20/20 + 7/20) x (33/33 + 7/33) x (48/48 + 7/48) x ...x (180/180 + 7/180)
= 16/9 x 27/20 x 40/33 x 55/48 x ......x 187/180
=
tới đây tự làm tiếp nha! Bí rồi! Chỉ gợi ý phần đầu thôi! Các bạn khác có gì lấy phần đầu bài của mình sau đó làm tiếp nha!
tính tổng\(A=\left(1+\frac{7}{9}\right).\left(1+\frac{7}{20}\right).\left(1+\frac{7}{33}\right)....\left(1+\frac{7}{2900}\right)\)
Tính:
\(C=\left(\frac{7}{9}+1\right)\left(\frac{7}{20}+1\right)\left(\frac{7}{33}+1\right)...\left(\frac{7}{10800}+1\right)\)
tính nhanh A= \(\left(\frac{7}{9}+1\right).\left(\frac{7}{20}+1\right).\left(\frac{7}{33}+1\right)....\left(\frac{7}{10800}+1\right)\)
Tính
\(A=\left(1+\frac{7}{9}\right)\left(1+\frac{7}{20}\right)\left(1+\frac{7}{33}\right)....\left(1+\frac{7}{2900}\right)\)
Cô giải như sau Minh nhé :)
\(A=\left(1+\frac{7}{9}\right)\left(1+\frac{7}{20}\right)\left(1+\frac{7}{33}\right)...\left(1+\frac{7}{2900}\right)=\frac{16}{9}.\frac{27}{20}.\frac{40}{33}...\frac{2907}{2900}\)
\(=\frac{8.2}{9.1}.\frac{9.3}{10.2}.\frac{10.4}{11.3}....\frac{57.51}{58.50}=\frac{\left(8.9.10....57\right)\left(2.3.4...51\right)}{\left(9.10.11...58\right)\left(2.3.4....50\right)}=\frac{8.51}{58}=\frac{204}{29}\)
( 1 + 7/9 ) x ( 1 + 7/20 ) x ( 1 + 7/33 ) x...x ( 1 + 7/2900)
= (8x2)/(9x1) x (9x3)/(10x2) x (10x4)/(11x3) x...x (57x51)(58x50)
=(8x2x9x3x10x4x...x57x51) / (9x1x10x2x11x3x...x58x50) Sau khi giản ước ta được :
= (8x51) / (1x58) = 204/29
\(A=\left(1+\frac{7}{9}\right)\left(1+\frac{7}{20}\right)\left(1+\frac{7}{33}\right)..........\left(1+\frac{7}{2900}\right)\)
\(A=\frac{16}{9}.\frac{27}{20}.\frac{40}{33}.......\frac{2907}{2900}\)
\(A=\frac{2.8}{1.9}.\frac{3.9}{2.10}.\frac{4.10}{3.11}......\frac{51.57}{50.58}\)
\(A=\frac{2.3.4.....51}{1.2.3...50}.\frac{8.9.10....57}{9.10.11...58}\)
\(A=51.\frac{8}{58}=\frac{204}{29}\)
Bạn Nguyễn Tuấn Minh làm đúng rùi đó !!! Chuẩn ý kiến mk...^.^
1.Tính
\(\left(1+\frac{7}{9}\right).\left(1+\frac{7}{20}\right).\left(1+\frac{7}{33}\right)....\left(1+\frac{7}{153}\right).\left(1+\frac{7}{180}\right)\)