\(3B=-1+\dfrac{1}{3}-\dfrac{1}{3^2}+..+\dfrac{1}{49}-\dfrac{1}{3^{50}}\)
3B+ B = -1 - \(\dfrac{1}{3^{51}}\)
4B= \(-1-\dfrac{1}{3^{51}}\)
B = \(\dfrac{-1-\dfrac{1}{3^{51}}}{4}\)
Thực hiện phép tính (tính nhanh nếu có thể):
a) \(\left(\dfrac{1}{2}-\dfrac{1}{3}\right)-\left(\dfrac{5}{3}-\dfrac{3}{2}\right)+\left(\dfrac{7}{3}-\dfrac{5}{2}\right)\)
b) \(\left(\dfrac{3}{4}-1\dfrac{1}{6}\right)^2:\sqrt{\dfrac{25}{144}}\)
Tính:
a/\(\dfrac{1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}}{1-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}}:\dfrac{3+\dfrac{3}{2}+\dfrac{3}{3}+\dfrac{3}{4}}{2-\dfrac{2}{2}+\dfrac{2}{3}-\dfrac{2}{4}}\)
b/\(\dfrac{1+\dfrac{1}{4}+\dfrac{1}{1+\dfrac{1}{4}}}{1-\dfrac{1}{4}-\dfrac{1}{1-\dfrac{1}{4}}}\)
c/\(\dfrac{\dfrac{2}{5}-\dfrac{7}{5}}{\dfrac{2}{5}-\dfrac{\dfrac{3}{4}}{\dfrac{3}{4}.\dfrac{3}{7}-1}}-\dfrac{1}{\dfrac{3}{7}\left(\dfrac{3}{4}.\dfrac{3}{7}.\dfrac{2}{5}-\dfrac{2}{5}-\dfrac{3}{4}\right)}\)
d/\(\left(\dfrac{\dfrac{4}{3}}{2+\dfrac{4}{3}}+\dfrac{2-\dfrac{4}{3}}{\dfrac{4}{3}}\right).\left(\dfrac{\dfrac{2}{3}}{4+\dfrac{2}{3}}-\dfrac{4-\dfrac{2}{3}}{\dfrac{2}{3}}\right)\)
Giúp mik với các bạn ơi 1 bài thôi cug đc.
\(\dfrac{x+4}{2000}+\dfrac{x+3}{2001}=\dfrac{x+2}{2002}+\dfrac{x+1}{2003}\)
1/* Chứng minh rằng:
\(\dfrac{1}{1\times2}+\dfrac{1}{3\times4}+\dfrac{1}{5\times6}+...\dfrac{1}{49\times50}=\dfrac{1}{26}+\dfrac{1}{27}+\dfrac{1}{28}+..+\dfrac{1}{50}\)
2/* Cho:
A=\(\dfrac{1}{1\times2}+\dfrac{1}{3\times4}+\dfrac{1}{5\times6}+.....+\dfrac{1}{99\times100}\). Chứng minh rằng:\(\dfrac{7}{12}< A>\dfrac{5}{6}\)
Các bn giúp mk những bài này nha!
10 Rút gọn:
a) A= 1+2+22+23+24+...+249+250
b) B= \(\dfrac{1}{2}+(\dfrac{1}{2})^2+(\dfrac{1}{2})^3+(\dfrac{1}{2})^4+(\dfrac{1}{2})^5+...+(\dfrac{1}{2})^{99}+(\dfrac{1}{2})^{100}\)
Tính:
\(\dfrac{\dfrac{1}{3}-\dfrac{1}{7}-\dfrac{1}{13}}{\dfrac{2}{3}-\dfrac{2}{7}-\dfrac{2}{13}}\times\dfrac{\dfrac{1}{3}-0,25+0,2}{1\dfrac{1}{6}-0,875+0,7}+\dfrac{6}{7}\)
Cho A= 1 + \(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{4034}\); B = 1 + \(\dfrac{1}{3}+\dfrac{1}{5}+\dfrac{1}{7}+...+\dfrac{1}{4033}\)
So sánh \(\dfrac{A}{B}\)với 1\(\dfrac{2017}{2018}\)
*Rút gọn
1) G=\(\dfrac{2}{3}+\dfrac{2}{3^3}+\dfrac{2}{3^5}+...+\dfrac{2}{3^{99}}\)
2) H=\(\dfrac{1}{2}-\dfrac{1}{2^4}+\dfrac{1}{2^7}-\dfrac{1}{2^{16}}+...-\dfrac{1}{2^{58}}\)
3) E=\(\dfrac{-1}{3}+\left(\dfrac{-1}{3}\right)^2+\left(\dfrac{-1}{3}\right)^3+...+\left(\dfrac{-1}{100}\right)^{100}\)
Cho B \(=\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{2015}}\)
CMR: \(B< \dfrac{1}{2}\)
a, D = \(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}\)
b, E = \(\dfrac{1}{1+2}+\dfrac{1}{1+2+3}+\dfrac{1}{1+2+3+4}+.......+\dfrac{1}{1+2+3+.......+9}\)
