cho mk hỏi:
\(E=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\)
Chứng minh rằng: a)\(\frac{1}{2}-\frac{1}{4}+\frac{1}{8}-\frac{1}{16}+\frac{1}{32}-\frac{1}{64}< \frac{1}{3}\)
b)\(\frac{1}{3}-\frac{2}{3^2}+\frac{3}{3^3}-\frac{4}{3^4}+...+\frac{99}{3^{99}}-\frac{100}{3^{100}}< \frac{3}{16}\)
Nhanh lên nhé! Mk đang cần gấp.
\(3B=1-\frac{2}{3}+\frac{3}{3^2}-\frac{4}{3^3}+...+\frac{99}{3^{98}}-\frac{100}{3^{99}}\)
\(B=\frac{1}{3}-\frac{2}{3^2}+\frac{3}{3^3}-\frac{4}{3^4}+...+\frac{99}{3^{99}}-\frac{100}{3^{100}}\)
\(\Rightarrow4B=3B+B=1-\frac{1}{3}+\frac{1}{3^2}-\frac{1}{3^3}+...+\frac{1}{3^{98}}-\frac{1}{3^{99}}-\frac{100}{3^{100}}\)
+ Đặt \(M=1-\frac{1}{3}+\frac{1}{3^2}-\frac{1}{3^3}+...+\frac{1}{3^{98}}-\frac{1}{3^{99}}\)
\(3M=3-1+\frac{1}{3}-\frac{1}{3^2}+...+\frac{1}{3^{97}}-\frac{1}{3^{98}}\)
\(\Rightarrow4M=3M+M=3-\frac{1}{3^{99}}\)
\(\Rightarrow M=\frac{3}{4}-\frac{1}{3^{99}\cdot4}\)
\(\Rightarrow4B=M-\frac{100}{3^{100}}=\frac{3}{4}-\frac{1}{3^{99}\cdot4}-\frac{100}{3^{100}}\)
\(\Rightarrow B=\frac{3}{16}-\frac{1}{3^{99}\cdot16}-\frac{100}{3^{100}\cdot4}\) \(\Rightarrow B< \frac{3}{16}\)
a) \(2A=1-\frac{1}{2}+\frac{1}{2^2}-\frac{1}{2^3}+\frac{1}{2^4}-\frac{1}{2^5}\)
\(A=\frac{1}{2}-\frac{1}{2^2}+\frac{1}{2^3}-\frac{1}{2^4}+\frac{1}{2^5}-\frac{1}{2^6}\)
\(\Rightarrow3A=2A+A=1-\frac{1}{2^6}\)
\(\Rightarrow A=\frac{1}{3}-\frac{1}{2^6\cdot3}< \frac{1}{3}\) ( đpcm )
bài 1 tìm x
a) \(\frac{1}{20}-\left(x-\frac{8}{5}\right)=\frac{1}{10}\) b) /x-\(\frac{3}{2}\)/=\(\frac{4}{3}\) c) /x-\(\frac{1}{3}\)/= / \(-\frac{5}{2}\)/ -\(\left(\frac{1}{4}-\frac{2}{3}\right)\)
d)/x-\(\frac{5}{8}\)/-\(\frac{3}{4}\)=0 e) /2.x+ \(\frac{5}{6}\)/= /\(\frac{1}{5}-\frac{2}{3}\)/+\(\frac{-3}{4}\)
giúp mk vs mk đang cần gấp
a: =>x-8/5=1/20-1/10=-1/20
=>x=-0,05+1,6=1,55
b: =>x-3/2=4/3 hoặc x-3/2=-4/3
=>x=17/6 hoặc x=1/6
c: =>\(\left|x-\dfrac{1}{3}\right|=\dfrac{5}{2}-\dfrac{1}{4}+\dfrac{2}{3}=\dfrac{35}{12}\)
=>x-1/3=35/12 hoặc x-1/3=-35/12
=>x=39/12=13/4 hoặc x=-31/12
d: =>|x-5/8|=3/4
=>x-5/8=3/4 hoặc x-5/8=-3/4
=>x=11/8 hoặc x=-1/8
a) \(\frac{x-3}{3}\)- 1= \(\frac{x}{-4}\)
b) \(\frac{5}{8}\)- (\(x-\frac{1}{2}\)) = \(\frac{-3}{4}\)
c) \(\frac{x}{38}-\frac{1}{19}=\frac{-1}{2}\)
d) \(\frac{x-3}{-15}+\left(x-1\right)=\frac{-5}{3}\)
e) \(\frac{x-8}{-6}+\frac{1}{2}=x-2\)
g) \(\frac{-6}{8}-\left(-x+\frac{1}{2}\right)=-3\)
h) \(x-\frac{1}{4}=\frac{-2}{14}+\frac{x}{2}\)
k) \(\left(x+3\right)-\left(x+\frac{1}{4}\right)=x\)
Làm hộ mk vs Mơn trước nhé
Nhanh mk tick
a) \(\frac{x-3}{3}-1=\frac{x}{-4}\)
\(\Leftrightarrow\frac{x-3}{3}-\frac{3}{3}=\frac{x}{-4}\)
\(\Leftrightarrow\frac{x-6}{3}=\frac{x}{-4}\)
\(\Leftrightarrow-4\left(x-6\right)=3x\)
\(\Leftrightarrow-4x+24=3x\)
\(\Leftrightarrow24=3x+4x\)
\(\Leftrightarrow7x=24\)
\(\Leftrightarrow x=\frac{24}{7}\)
b) \(\frac{5}{8}-\left(x-\frac{1}{2}\right)=\frac{-3}{4}\)
\(\Leftrightarrow\frac{5}{8}-x+\frac{1}{2}=\frac{-3}{4}\)
\(\Leftrightarrow\frac{5}{8}+\frac{4}{8}-x=\frac{-3}{4}\)
\(\Leftrightarrow\frac{9}{8}-x=\frac{-3}{4}\)
\(\Leftrightarrow x=\frac{9}{8}+\frac{3}{4}\)
\(\Leftrightarrow x=\frac{15}{8}\)
c) \(\frac{x}{38}-\frac{1}{19}=\frac{-1}{2}\)
\(\Leftrightarrow\frac{x}{38}-\frac{2}{38}=\frac{-1}{2}\)
\(\Leftrightarrow\frac{x-2}{38}=\frac{-1}{2}\)
\(\Leftrightarrow2\left(x-2\right)=-38\)
\(\Leftrightarrow2x-4=-38\)
\(\Leftrightarrow2x=-38+4\)
\(\Leftrightarrow2x=-34\)
\(\Leftrightarrow x=-34\div2\)
\(\Leftrightarrow x=-17\)
tim x
a)\(2\frac{3}{4}x-1\frac{5}{8}x=1\)
b)\(2\frac{3}{4}x-1\frac{5}{8}x=1\)
c)\(\frac{3}{2}x-\frac{2}{5}=\frac{1}{3}x-\frac{1}{4}\)
d)\(2x-\frac{1}{4}=\frac{5}{6}-\frac{1}{2}x\)
e)\(\frac{-5}{6}+3x=\frac{2}{3}-\frac{1}{2}x\)
f)\(\frac{5}{2}x-\frac{3}{2}=x+\frac{29}{10}\)
g)\(\frac{2}{3}+\frac{7}{3}x=\frac{5}{4}x+\frac{1}{6}\)
h)\(\frac{1}{3}.x+\frac{2}{5}\left(x-1\right)=0\)
giup mk nha moi nguoi
\((\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}).x=\frac{1}{9}+\frac{2}{8}+\frac{3}{7}+...+\frac{8}{2}+\frac{9}{1}\)
Ai bt làm thì giúp mk với!
Đặt \(A=\frac{1}{9}+\frac{2}{8}+...+\frac{8}{2}+\frac{9}{1}\)
\(\Rightarrow A=\frac{1}{9}+\frac{2}{8}+\frac{3}{7}+...+\frac{8}{2}+\left(1+1+...+1\right)\left(9cs1\right)\)
\(\Rightarrow A=\left(\frac{1}{9}+1\right)+\left(\frac{2}{8}+1\right)+...+\left(\frac{8}{2}+1\right)+1\)
\(\Rightarrow A=\frac{10}{9}+\frac{10}{8}+...+\frac{10}{2}+\frac{10}{10}\)
\(\Rightarrow A=10.\left(\frac{1}{2}+...+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}\right)\)
Mà \(\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{10}\right).x=A\)
\(\Rightarrow\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}\right).x=\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{10}\right).10\)
\(\Rightarrow x=10\)
Vậy \(x=10\)
Bài 1: Tính
a)\(\frac{1}{3}+\frac{3}{8}-\frac{7}{12}\)
b) \(\frac{3}{14}+\frac{5}{8}-\frac{1}{2}\)
c) \(\frac{1}{4}-\frac{2}{3}-\frac{11}{18}\)
d) \(\frac{1}{4}+\frac{5}{12}-\frac{1}{13}-\frac{7}{8}\)
#giải hộ mk vs mk đng cần gấp
a) MC :24
\(\frac{1}{3}+\frac{3}{8}-\frac{7}{12}=\frac{1\times8+3\times3-7\times2}{24}=\frac{3}{24}=\frac{1}{8}\)
b)MC : 56
\(\frac{3}{14}+\frac{5}{8}-\frac{1}{2}=\frac{3\times4+5\times7-1\times28}{56}=\frac{19}{56}\)
c) MC: 36
\(\frac{1}{4}-\frac{2}{3}-\frac{11}{18}=\frac{1\times9-2\times12-11\times2}{36}=\frac{-37}{36}\)
d) MC: 312
\(\frac{1}{4}+\frac{5}{12}-\frac{1}{13}-\frac{7}{8}=\frac{1\times78+5\times26-1\times24-7\times39}{312}=\frac{-89}{312}\)
\(d,\left(\frac{1}{6}+2\frac{1}{12}-10,75\right).x-7=\left(\frac{2}{5}+\frac{3}{8}+0,225\right):0,1\)\(c,1-\left(5\frac{3}{8}+x-7\frac{5}{24}\right):16\frac{2}{3}=0\)
\(e,\frac{3}{2}x-70\frac{10}{11}:\left(\frac{131313}{151515}+\frac{131313}{353535}+\frac{131313}{636363}+\frac{131313}{999999}\right)=-5\)\(f,0,25x\left(\frac{8}{5}:1\frac{1}{2}+\frac{1}{50}\right)=\frac{7}{50}\left(2,91+0,09\right).4\)
ai làm nhanh và đúng mk tick cho
bài 1 tìm x
a) \(\frac{1}{20}-\left(x-\frac{8}{5}\right)=\frac{1}{10}\) b) /x-\(\frac{3}{2}\)/=\(\frac{4}{3}\) c) /x-\(\frac{1}{3}\)/= / \(-\frac{5}{2}\)/ -\(\left(\frac{1}{4}-\frac{2}{3}\right)\)
d)/x-\(\frac{5}{8}\)/-\(\frac{3}{4}\)=0 e) /2.x+ \(\frac{5}{6}\)/= /\(\frac{1}{5}-\frac{2}{3}\)/+\(\frac{-3}{4}\)
giúp mk vs mk đang cần gấp
Hu hu... mọi người oi, giúp mk vói nà. Mk gấp lém nà. Hạn là mai nộp òi nà. Đề nà nà:
1) Tính: A= \(-\frac{7}{12}+\frac{11}{8}-\frac{5}{9}\)
B=\(\frac{1}{7}-\frac{8}{7}.8-3:\frac{3}{4}.\left(-2\right)^2\)
C=\(1,4.\frac{15}{49}-\left(\frac{4}{5}+\frac{2}{3}\right):2\frac{1}{5}\)
2) Tìm x, y biết:
a) \(\frac{2}{3}:x+\frac{1}{2}=\frac{1}{10}\)
b)\(\left(3\frac{4}{5}-2.x\right).1\frac{1}{3}=5\frac{5}{7}\)
c)\(\frac{x}{7}=\frac{6}{-21}\)
d)\(\frac{x-1}{5}=\frac{4}{y}\)/ x,y thuộc Z
e) \(\frac{x}{y}=\frac{4}{y}\)/ x,y thuộc Z
3) Để cứu trợ đồng bào bị hạn hán, 1 tổ chức từ thiện đề ra mục tiêu khuyên góp đc 8400 kg gạo. Trong 3 tuần đầu, họ khuyên đc 1/2 số gạo. Sau đó khuyên đc 2/3 số gạo đó. Cuối cùng khuyên đc 1/4 số gạo đó.
Hỏi họ vượt mức đề ra ko?