Đại số lớp 7
Các câu hỏi tương tự
*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=\(\dfrac{-1}{3}+\left(\dfrac{-1}{3}\right)^2+\left(\dfrac{-1}{3}\right)^3+...+\left(\dfrac{-1}{100}\right)^{100}\)
CMR: \(\dfrac{1}{3}+\dfrac{2}{3^2}+\dfrac{3}{3^3}+...+\dfrac{100}{3^{100}}< \dfrac{1}{2}\)
Chứng minh: \(\dfrac{1}{3}+\dfrac{2}{3^2}+\dfrac{3}{3^3}+...+\dfrac{100}{3^{100}}< \dfrac{1}{2}\)
A = \(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+......+\dfrac{1}{2^{100}}\)
B = \(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+....+\dfrac{1}{100^2}\)
mk cần gấp
VT
15 tháng 12 2021 lúc 21:44
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) \(\left(\dfrac{3}{4}-1\dfrac{1}{6}\right)^2:\sqrt{\dfrac{25}{144}}\)
Chứng minh rằng:
\(\dfrac{1}{3}+\dfrac{2}{3^2}+\dfrac{3}{3^3}+...+\dfrac{100}{3^{100}}< \dfrac{3}{4}\)
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-d...
Đọc tiếp
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.
1/ Tính
dfrac{left(1+2+3+...+100right).left(dfrac{1}{3}-dfrac{1}{5}-dfrac{1}{7}-dfrac{1}{9}right).left(6,3.12-21.3,6right)}{dfrac{1}{2}+dfrac{1}{3}+dfrac{1}{4}+...+dfrac{1}{100}}
2/ Tìm x:
dfrac{x+4}{2000}+dfrac{x+3}{2001}dfrac{x+2}{2002}+dfrac{x+1}{2003}
3/ Cho Adfrac{1}{1.2}+dfrac{1}{3.4}+dfrac{1}{5.6}+...+dfrac{1}{99.100}
Chứng minh: dfrac{7}{12} A dfrac{5}{6}
4/ Tìm a,bvarepsilon Q:a+ba.ba:b
Giúp mik nha mai mik cần rồi.
Đọc tiếp
1/ Tính
\(\dfrac{\left(1+2+3+...+100\right).\left(\dfrac{1}{3}-\dfrac{1}{5}-\dfrac{1}{7}-\dfrac{1}{9}\right).\left(6,3.12-21.3,6\right)}{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{100}}\)
2/ Tìm x:
\(\dfrac{x+4}{2000}+\dfrac{x+3}{2001}=\dfrac{x+2}{2002}+\dfrac{x+1}{2003}\)
3/ Cho \(A=\dfrac{1}{1.2}+\dfrac{1}{3.4}+\dfrac{1}{5.6}+...+\dfrac{1}{99.100}\)
Chứng minh: \(\dfrac{7}{12}< A< \dfrac{5}{6}\)
4/ Tìm \(a,b\varepsilon Q:a+b=a.b=a:b\)
Giúp mik nha mai mik cần rồi.
10 Rút gọn:
a) A= 1+2+22+23+24+...+249+250
b) B= \(\dfrac{1}{2}+(\dfrac{1}{2})^2+(\dfrac{1}{2})^3+(\dfrac{1}{2})^4+(\dfrac{1}{2})^5+...+(\dfrac{1}{2})^{99}+(\dfrac{1}{2})^{100}\)