tính nhanh
\(P=\frac{3}{1.5}+\frac{3}{5.9}+\frac{3}{9.13}+...+\frac{3}{197.101}\)
Tính M:
\(\frac{3}{1.5}+\frac{3}{5.9}+\frac{3}{9.13}+.............+\frac{3}{3993.3997}+\frac{3}{3997.4001}\)
3/1*5+3/5*9+3/9*13+.....+3/3993*3997+3/3997*4001
=1/3(1-1/5+1/5-1/9+1/9-1/13+....+1/3993-1/3997+1/3997-1/4001)
=1/3(1-1/4001)
=4000/12003
k nha
= 3/4(1-1/5+1/5-1/9+1/9-1/13+...+1/3993-1/3997+1/3997-1/4001)
=3/4(1-1/4001)
=3000/4001
\(\frac{3}{1.5}+\frac{3}{5.9}+\frac{3}{9.13}+...+\frac{3}{21.25}\)
\(\frac{3}{1.5}+\frac{3}{5.9}+\frac{3}{9.13}+......+\frac{3}{21.25}\)
\(=\frac{3}{4}\left(\frac{4}{1.5}+\frac{4}{5.9}+\frac{4}{9.13}+.....+\frac{4}{21.25}\right)\)
\(=\frac{3}{4}\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+......+\frac{1}{21}-\frac{1}{25}\right)\)
\(=\frac{3}{4}\left(1-\frac{1}{25}\right)\)
\(=\frac{3}{4}.\frac{24}{25}\)
\(=\frac{18}{25}\)
\(4A=3-\frac{1}{5}+\frac{3}{5}-\frac{3}{9}+\frac{3}{9}-\frac{3}{13}+...+\frac{3}{21}-\frac{3}{25}\)\(\frac{3}{25}\)
\(4A=3-\frac{3}{25}\)
\(4A=\frac{72}{25}\)
\(A=\frac{18}{25}\)
k minh ha
\(giải:\)
\(\frac{3}{1.5}+\frac{3}{5.9}+\frac{3}{9.13}+...+\frac{3}{21.25}\)
\(=3\left(\frac{1}{1.5}+\frac{1}{5.9}+\frac{1}{9.13}+...+\frac{3}{21.25}\right)\)
\(=\frac{3}{4}\left(\frac{4}{1.5}+\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{21.25}\right)\)
\(=\frac{3}{4}\left(\frac{1}{1}-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{21}-\frac{1}{25}\right)\)
\(=\frac{3}{4}\left(1-\frac{1}{25}\right)\)
\(=\frac{3}{4}.\frac{24}{25}\)
\(=\frac{18}{25}\)
\(\frac{3}{1.5}+\frac{3}{5.9}+\frac{3}{9.13}+....+\frac{3}{101.105}\)
chú thích: dấu " . " là dấu nhân
các bạn giúp mik nhé
\(A=3\times\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{101}-\frac{1}{105}\right)\)
\(A=3\times\left(1-\frac{1}{105}\right)\)
\(A=3\times\frac{104}{105}\)
\(A=\frac{104}{35}\)
II) Tính nhanh:
a)\(\frac{3^2}{1.4}+\frac{3^2}{4.7}+\frac{3^2}{7.10}+...+\frac{3^2}{61.64}\)
b)\(\frac{1}{1.5}+\frac{1}{5.9}+\frac{1}{9.13}+...+\frac{1}{21.25}\)
c)\(\frac{2^2}{1.3}+\frac{3^2}{2.4}+\frac{4^2}{3.5}+...+\frac{20^2}{19.21}\)
nhanh choa tick * đg rất tức giận*
a) \(=\frac{9}{1.4}+\frac{9}{4.7}+\frac{9}{7.10}+...+\frac{9}{61.64}\)
\(=3\left(\frac{1}{1}-\frac{1}{64}\right)\)
\(=\frac{189}{64}\)
b) \(=\frac{1}{1}-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+...+\frac{1}{21}-\frac{1}{25}\)
\(=\frac{1}{1}-\frac{1}{25}\)
\(=\frac{24}{25}\)
c) Chưa học tới
b)1/1.5+1/5.9+1/9.13+...+1/21.25
=1/4.(4/1.5+4/5.9+4/9.13+4/21.25)
=1/4.(4-4/5+4/5-4/9+4/9-4/13+...+4/21-4/25)
=1/4.(4-4/25)
=1/4.(100/25-4/25)
=1/4.96/25
=24/25
C = \(\frac{2}{4.7}-\frac{3}{5.9}+\frac{2}{7.10}-\frac{3}{9.13}+...+\frac{2}{301.304}-\frac{3}{401.405}\)
tính c
TẬP HỢP RA HAI NHÓM .MỘT NHÓM SỐ ÂM.CÒN NHÓM KIA LÀ SỐ DƯƠNG MÀ TÍNH
STUDY WELL
K NHA
MK XIN CẢM ƠN CÁC BẠN NHÌU
C = 24.7 −35.9 +27.10 −39.13 +...+2301.304 −3401.405
\(C=\left(\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{301.304}\right)-\left(\frac{3}{5.9}+\frac{3}{9.13}+...+\frac{3}{401.405}\right)\)
\(C=\frac{2}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{301}-\frac{1}{304}\right)-\frac{3}{4}\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{401}-\frac{1}{405}\right)\)
\(C=\frac{2}{3}\left(\frac{1}{4}-\frac{1}{304}\right)-\frac{3}{4}\left(\frac{1}{5}-\frac{1}{405}\right)\)
\(C=\frac{2}{3}.\frac{75}{304}-\frac{3}{4}.\frac{16}{81}\)
\(C=\frac{25}{152}-\frac{4}{27}\)
\(C=\frac{67}{4104}\)
Study well
\(C=\frac{2}{4\cdot7}-\frac{3}{5\cdot9}+\frac{2}{7\cdot10}-\frac{3}{9\cdot13}+...+\frac{2}{301\cdot304}-\frac{3}{401\cdot405}\)
\(C=\left(\frac{2}{4\cdot7}+\frac{2}{7\cdot10}+...+\frac{2}{301\cdot304}\right)-\left(\frac{3}{5\cdot9}+\frac{3}{9\cdot13}+...+\frac{3}{401\cdot405}\right)\)
\(C=\frac{2}{3}\left(\frac{3}{4\cdot7}+\frac{3}{7\cdot10}+...+\frac{3}{301\cdot304}\right)-\frac{3}{4}\left(\frac{4}{5\cdot9}+\frac{4}{9\cdot13}+...+\frac{4}{401\cdot405}\right)\)
\(C=\frac{2}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{301}-\frac{1}{304}\right)-\frac{3}{4}\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{401}-\frac{1}{405}\right)\)
\(C=\frac{2}{3}\left(\frac{1}{4}-\frac{1}{304}\right)-\frac{3}{4}\left(\frac{1}{5}-\frac{1}{405}\right)\)
\(C=\frac{2}{3}\cdot\frac{77}{304}-\frac{3}{4}\cdot\frac{82}{405}\)
\(C=\frac{77}{456}-\frac{41}{270}\)
\(C=\frac{349}{20520}\)
Không chắc =))
bài 3: chứng tỏ rằng:
\(\frac{4}{1.5}+\frac{4}{5.9}+\frac{4}{9.13}....\frac{4}{2005.2009}\)
toán 6 giúp mình với
Giải:
Ta có công thức sau:
\(\frac{k}{a.b}=\frac{1}{a}-\frac{1}{b}\) với b - a = k hoặc a - b = k
Lắp vào biểu thức A, ta có:
\(A=\frac{4}{1.5}+\frac{4}{5.9}+\frac{4}{9.14}+...+\frac{4}{2005.2009}\\ =\frac{1}{1}-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{2001}-\frac{1}{2005}+\frac{1}{2005}-\frac{1}{2009}\)
\(=1+\left(\frac{1}{5}-\frac{1}{5}\right)+\left(\frac{1}{9}-\frac{1}{9}\right)+...+\left(\frac{1}{2005}-\frac{1}{2005}\right)-\frac{1}{2009}\\ =1-\frac{1}{2009}\\ =\frac{2009-1}{2009}\\ =\frac{2008}{2009}\)
Vậy \(A=\frac{2008}{2009}\)
Chúc bạn học tốt!
4/1.5+4/5.9+4/9.13+…4/2005.2009
=1/1-1/5+1/5-1/9+1/9-1/13+…+1/2005-1/2009
=1-1/2009=2008/2009
x+\(\frac{3}{5.9}+\frac{3}{9.13}+\frac{3}{13.17}+...+\frac{4}{41.45}=-\frac{37}{45}\)
\(x+\frac{3}{5.9}+\frac{3}{9.13}+\frac{3}{13.17}+...+\frac{4}{41.45}=-\frac{37}{45}\)
\(\Leftrightarrow x+3\left(\frac{1}{5.9}+\frac{1}{9.13}+\frac{1}{13.17}+...+\frac{1}{41.45}\right)=-\frac{37}{45}\)
\(\Leftrightarrow x+\frac{3}{4}\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+...+\frac{1}{41}-\frac{1}{45}\right)=-\frac{37}{45}\)
\(\Leftrightarrow x+\frac{3}{4}\left(\frac{1}{5}-\frac{1}{45}\right)=-\frac{37}{45}\)
\(\Leftrightarrow x+\frac{3}{4}.\frac{8}{45}=-\frac{37}{45}\)
\(\Leftrightarrow x+\frac{2}{15}=-\frac{37}{45}\)
\(\Leftrightarrow x=-\frac{43}{45}\)
C=\(\frac{2}{4.7}-\frac{3}{5.9}+\frac{2}{7.10}-\frac{3}{9.13}+...........+\frac{2}{301.304}-\frac{3}{401.405}\)
Các bạn ơi trả lời giúp mình nhanh nhanh nha!
Ai trả lời đúng mình sẽ tick
\(C=\frac{2}{4.7}-\frac{3}{5.9}+\frac{2}{7.10}-\frac{3}{9.13}+...+\frac{2}{301.304}-\frac{3}{401.405}\)
\(C=\left(\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{301.304}\right)-\left(\frac{3}{5.9}+\frac{3}{9.13}+...+\frac{3}{401.405}\right)\)
\(C=\frac{2}{3}\left(\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{301.304}\right)-\frac{3}{4}\left(\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{401.405}\right)\)
\(C=\frac{2}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{301}-\frac{1}{304}\right)-\frac{3}{4}\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+..+\frac{1}{401}-\frac{1}{405}\right)\) \(C=\frac{2}{3}\left(\frac{1}{4}-\frac{1}{304}\right)-\frac{3}{4}\left(\frac{1}{5}-\frac{1}{405}\right)\)
\(C=\frac{25}{152}-\frac{4}{27}\)
\(C=\frac{67}{4104}\)
Tính tổng sau:
M=\(\frac{4}{1.5}-\frac{4}{5.9}-\frac{4}{9.13}-.....-\frac{4}{\left(n-4\right).n}\)
Ai nhanh mk tick
M=\(\frac{4}{1.5}-\frac{4}{5.9}-\frac{4}{9.13}-...-\frac{4}{\left(n-4\right).n}\)
\(M=1-\frac{1}{5}-\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+...+\frac{1}{n-4}-\frac{1}{n}\right)\)
\(M=1-\frac{1}{5}-\frac{1}{5}+\frac{1}{n}\)
\(M=\frac{3}{5}+\frac{1}{n}\)
Mình chỉ giải đến đây thôi vì chẳng biết n bằng mấy cả
= - (1-1/5 +1/5 -1/9 +1/9 -1/13 +1/n + 1/n+4)
=-(1-1/n+4)
=-1+1/n+4
Phạm Thị Mai Anh ko có dấu( - )đằng trước đâu ạ