a) (1-1/15) x (1-1/21) x (1-1/28) x ... x (1-1/79800)
b) (1-1/122) x ( 1-1/132) x (1-1/142) x ... x (1-1/802)
Mình đag cần gấp
A= (1-1/15) x (1-1/21) x (1-1/28) x ... x (1-1/79800)
Mình đag cần gấp
\(A=\left(1-\frac{1}{15}\right)\left(1-\frac{1}{21}\right)\left(1-\frac{1}{28}\right)...\left(1-\frac{1}{79800}\right)\)
\(A=\frac{14}{15}.\frac{20}{21}.\frac{27}{28}...\frac{209}{210}\)
\(A=\frac{28}{30}.\frac{40}{42}.\frac{54}{56}...\frac{418}{240}\)
\(A=\frac{4.7}{5.6}.\frac{5.8}{6.7}.\frac{6.9}{7.8}...\frac{19.22}{20.21}\)
\(A=\frac{4.5.6...19}{5.6.7...20}.\frac{7.8.9...22}{6.7.8...21}\)
\(A=\frac{4}{20}.\frac{22}{6}\)
\(A=\frac{11}{15}\)
( 1-1/15)x(1-1/21)x(1-1/28)x...x(1-1/210) giúp mình với mình cần gấp
=14/15*20/21*...*209/210
\(=\dfrac{4\cdot7}{5\cdot6}\cdot\dfrac{5\cdot8}{6\cdot7}\cdot...\cdot\dfrac{19\cdot22}{20\cdot21}\)
\(=\dfrac{4\cdot5\cdot6\cdot...\cdot19}{5\cdot6\cdot7\cdot...\cdot20}\cdot\dfrac{7\cdot8\cdot9\cdot...\cdot22}{6\cdot7\cdot8\cdot...\cdot21}=\dfrac{11}{15}\)
( 1-1/15)x(1-1/21)x(1-1/28)x...x(1-1/210) giúp mình với ( mình đg cần gấp)
Bài 2 : Tính
a) A= (1- 1/42) x (1-1/52) x (1-1/62) x ... x (1-1/2002)
b) B= 3/35 x 15/63 x 35/99 x ... x 9999/10815
Mình đag cần gấp
a) CÓ: A = (1-1/42).(1-1/52).(1-1/62)......(1-1/2002)
=\(\frac{4^2-1^2}{4^2}\). \(\frac{5^2-1^2}{5^2}\). \(\frac{6^2-1^2}{6^2}\)....... \(\frac{200^2-1^2}{200^2}\)
Ta có công thức sau : a2-b2= a2 -ab+ab-b2
= a(a-b) + b(a-b)
= (a+b)(a-b)
ÁP DỤNG CÔNG THỨC TRÊN VÀO BÀI TOÁN TA ĐƯỢC :
A= \(\frac{3.5}{4^2}\). \(\frac{4.6}{5^2}\). \(\frac{5.7}{6^2}\)......\(\frac{199.201}{200^2}\)
= \(\frac{\left(3.4.5.....199\right)\left(5.6.7....201\right)}{\left(4.5.6......200\right)^2}\)
= \(\frac{\left(3.4.5.......199\right)\left(5.6.7.....200.201\right)}{\left(4.5.6.....199.200\right)\left(4.5.6......200\right)}\)
= \(\frac{3.201}{200.4}\)
= \(\frac{603}{800}\)
b)Từ đề bài ta suy ra : B=\(\frac{1.3}{5.7}\).\(\frac{3.5}{7.9}\). \(\frac{5.7}{9.11}\)...... \(\frac{99.101}{103.105}\)
= \(\frac{1.3^2.5^2.7^2......99^2.101}{5.7^2.9^2.11^2....99^2.101^2.103^2.105}\)
=\(\frac{3^2.5}{101.103^2.105}\)
=\(\frac{3}{7500563}\)
Cho A= (1-1/2) x (1-1/4) x (1-1/6) x (1-1/8) x ... x (1-1/195). Chứng minh rằng A< 1/14
mình đag cần gấp
A= (1-1/2) x (1-1/4) x (1-1/6) x (1-1/8) x ... x (1-1/195). Chứng minh rằng A < 1/14
Mình đag cần gấp
E= (1/12 + 1) x (1/13 +1) x (1/14 + 1) x ... x (1/199 +1 )
Mình đag cần gấp
E=13/12.14/13....200/199=200/12=50/3
TÍNH NHANH
a) 3/16 + 4/15 + 5/16 + 1/15
b) 6/7 x 8/15 x 7/6 x 15/16
c) 19/20 x 13/21 + 9/20 x 8/21
d) (1+ 10/15 ) x (1+ 1/16 ) x ( 1+ 1/17 ) x ( 1+ 1/18 )
MINK ĐANG CẦN GẤP
a) \(\frac{3}{16}+\frac{4}{15}+\frac{5}{16}+\frac{1}{15}\)
\(=\left(\frac{3}{16}+\frac{5}{16}\right)+\left(\frac{4}{15}+\frac{1}{15}\right)\)
\(=\frac{1}{2}+\frac{1}{3}\)
\(=\frac{5}{6}\)
b) \(\frac{6}{7}\times\frac{8}{15}\times\frac{7}{6}\times\frac{15}{16}\)
\(=\left(\frac{6}{7}\times\frac{7}{6}\right)\times\left(\frac{8}{15}\times\frac{15}{16}\right)\)
\(=1\times\frac{1}{2}=\frac{1}{2}\)
c) \(\frac{19}{20}\times\frac{13}{21}+\frac{9}{20}\times\frac{8}{21}\)
\(=\frac{19\times13}{20\times21}+\frac{9\times8}{20\times21}\)
\(=\frac{247}{420}+\frac{72}{420}\)
\(=\frac{319}{420}\)
tích cho chị nha
câu a) = 5/6
câu b = 1/2
câu c = 319/420
B= (1-1/122) x (1-1/132) x (1-1/142) x ... x (1-1/802)
Mình đag cần gấp
B=143/144.168/169.....6399/6400
=11.13/12.12 . 12.14/13.13 .....79.81/80.80
=11.12....79/12.13...80 . 13.14......81/12.13....80
=11/80 . 81/12=297/320