Tính các tổng sau:
B= \(\frac{5.7}{2.7}+\frac{3.7}{7.10}+\frac{6.7}{10.16}+\frac{7}{16.17}+\frac{2.7}{17.19}\)
giúp mình 2 bài tính tổng nữa nha:
A= \(\frac{2}{1.3}\) + \(\frac{2}{3.5}\) + \(\frac{2}{5.7}\) +...+ \(\frac{2}{2009.2011}\) + \(\frac{2}{2011.2013}\)
B= \(\frac{5.7}{2.7}\) + \(\frac{3.7}{7.10}\) + \(\frac{6.7}{10.16}\) + \(\frac{7}{16.17}\) + \(\frac{2.7}{17.19}\)
Sễ thui:
A = 1 - 1/3 + 1/3 - 1/5 + ........ + 1/2011 - 1/2013
= 1- 1/2013
= 2012/2013
\(A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2011}-\frac{1}{2013}\)
\(A=1-\frac{1}{2013}\)
\(A=\frac{2012}{2013}\)
phần B nhân hạng tử 1 số nào đó tự tìm nhe ^^
Tính tổng:
C=\(\frac{3}{1.5}+\frac{3}{5.9}+\frac{3}{9.13}+...+\frac{3}{101.105}\)
D=\(\frac{4}{2.7}+\frac{4}{7.12}+\frac{4}{12.17}+...+\frac{4}{102.107}\)
E=\(\frac{5}{3.7}+\frac{5}{7.11}+\frac{5}{11.15}+...+\frac{5}{103.107}\)
F=\(\frac{6}{2.7}+\frac{6}{7.12}+\frac{6}{12.17}+...+\frac{6}{102.107}\)
Chỉ cần để các thừa số ra ngoài rồi nhân các số mà bằng khoảng cách của mẫu lên tử là giải được
LÀM TẮT NHÉ :
\(C=\frac{3}{4}\left(\frac{1}{1}-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+...+\frac{1}{101}-\frac{1}{105}\right)\))
\(D=\frac{4}{5}\left(\frac{1}{2}-\frac{1}{7}+...+\frac{1}{102}-\frac{1}{107}\right)\)
tương tự với các phần còn lại
Tính
a) \(\frac{8^{20}+4^{20}}{4^{25}+6^{45}}\)
b) \(\frac{-5.7^5+7^4}{7^6.10-2.7^5}\)
Giúp mk zới
b) \(\frac{-5\cdot7^5+7^4}{7^6\cdot10-2\cdot7^5}\)
\(=\frac{-35\cdot7^4+7^4}{7^5\cdot70-2\cdot7^5}\)
\(=\frac{7^4\left(-35+1\right)}{7^5\left(70-2\right)}\)
\(=\frac{7^4\cdot\left(-34\right)}{7^5\cdot68}\)
\(=\frac{-1}{14}\)
Chắc sai =))
Tính :
\(S=\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+\frac{5}{7.9}+...+\frac{5}{17.19}\)
S = \(\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+\frac{5}{7.9}+.......+\frac{5}{17.19}\)
S : 5 = \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+.....+\frac{1}{17.19}\)
S : 5 = \(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}+.......+\frac{1}{17}-\frac{1}{19}\)
=> S : 5 = 1 - \(\frac{1}{19}=\frac{19}{19}-\frac{1}{19}=\frac{18}{19}\)
=> S = \(\frac{18}{19}x5=\frac{90}{19}\)
Tính tổng:
a)\(\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{24.25}\)
b)\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{99.101}\)
1/5.6 + 1/6.7 + 1/7.8 +...+ 1/24.25
=1/5 - 1/6 + 1/6-1/7 +1/7-1/8 + ... + 1/24-1/25
=> Kết quả là: 1/5 - 1/25 = 4/25
b) 2/1.3 + 2/3.5 + 2/5.7 + 2/7.9+...+ 2/99.101
=2/1-2/3 + 2/3-2/5 + 2/5-2/7 + 2/7-2/9 + ... + 2/99-2/101
=> kết quả là 2/1 - 2/101 =200/101
a) \(\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{24.25}\)
=\(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{24}-\frac{1}{25}\)
=\(\frac{1}{5}-\frac{1}{25}\)
=\(\frac{4}{25}\)
b)\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{99.101}\)
=\(2.\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{99.101}\right)\)
=\(2.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{99}-\frac{1}{101}\right)\)
=\(2.\left(\frac{1}{1}-\frac{1}{101}\right)\)
=\(2.\frac{100}{101}\)
=\(\frac{200}{101}\)
a)\(\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{24.25}\)
\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{24}-\frac{1}{25}\)
\(=\frac{1}{5}-\frac{1}{25}\)
\(=\frac{5}{25}-\frac{1}{25}\)
\(=\frac{4}{25}\)
b) \(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{99.101}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{99}-\frac{1}{101}\)
\(=1-\frac{1}{101}\)
\(=\frac{101}{101}-\frac{1}{101}\)
\(=\frac{100}{101}\)
Tìm x,y,z:
a) 2.7x+1-3.7x=77
b)\(\frac{x+5}{3}=\frac{27}{x+5}\)
c)\(\frac{2}{3}x=\frac{3}{4}y=\frac{4}{5}zv\text{ã}-y+z=34\)
a,2.7x+1-3.7x=77
=>2.7x.71-3.7x=77
=>7X.(2.7-3)=77
=>7x.11=77
=>7x=7
=>7x=71
=>x=1
rút gọn
a)
\(\frac{2^3.3^4}{2^2.3^2.5}\)
b)
\(\frac{2^4.5^2.11^2.7}{2^3.5^3.7^2.11}\)
TA CÓ : \(\frac{2^3.3^4}{2^2.3^2.5}\)= \(\frac{2^3.3^4}{\left(2.3\right)^2.5}\)= \(\frac{2^3.3^4}{6^2.5}\)= \(\frac{2^3.3^4}{36.5}\)= \(\frac{8.81}{180}\)= \(\frac{648}{180}\)= 648 : 180 = 3,6 HOẶC \(\frac{648}{180}\)= \(\frac{18}{5}\)
ngu..............................
tao lao
\(F=\frac{11}{1.3}+\frac{47}{3.5}+\frac{107}{5.7}+\frac{191}{7.9}+...+\frac{971}{17.19}\)
Tính tổng:
A=\(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{99.101}\)
B=\(\frac{2}{4.7}+\frac{2}{7.10}+\frac{2}{10.13}+...+\frac{2}{100.103}\)
\(A=\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+...+\frac{1}{99\cdot101}\)
\(A=\frac{1}{2}\cdot\left(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{99\cdot101}\right)\)
\(A=\frac{1}{2}\cdot\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{99}-\frac{1}{101}\right)\)
\(A=\frac{1}{2}\cdot\left(\frac{1}{3}-\frac{1}{101}\right)=\frac{1}{2}\cdot\frac{97}{303}=\frac{97}{606}\)
\(B=\frac{2}{4\cdot7}+\frac{2}{7\cdot10}+\frac{2}{10\cdot13}+...+\frac{2}{100\cdot103}\)
\(B=\frac{2}{3}\cdot\left(\frac{3}{4\cdot7}+\frac{3}{7\cdot10}+\frac{3}{10\cdot13}+...+\frac{3}{100\cdot103}\right)\)
\(B=\frac{2}{3}\cdot\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{100}-\frac{1}{103}\right)\)
\(B=\frac{2}{3}\cdot\left(\frac{1}{4}-\frac{1}{103}\right)=\frac{2}{3}\cdot\frac{99}{412}=\frac{33}{206}\)