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4A=\(\frac{4}{3.7}+\frac{4}{7.11}+...+\frac{4}{107.111}\)
4A=\(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{107}-\frac{1}{111}\)
4A=\(\frac{1}{3}-\frac{1}{111}=\frac{12}{37}\)
A=\(\frac{12}{37}:4=\frac{12}{37}.\frac{1}{4}=\frac{3}{37}\)
Ta có A = \(\frac{4}{3.7}+\frac{4}{7.11}+..............+\frac{4}{107.111}\)
=> A = \(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+.............+\frac{1}{107}-\frac{1}{111}\)
A = \(\frac{1}{3}-\frac{1}{111}=\frac{12}{37}\)
k nha bạn
\(A=\frac{4^2}{3.7}+\frac{4^2}{7.11}+\frac{4^2}{11.15}+...+\frac{4^2}{107.111}\)
\(A=\) \(4\left(\frac{1}{3.7}+\frac{1}{7.11}+\frac{1}{11.15}+...+\frac{1}{107.111}\right)\)
\(A=4\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{107}-\frac{1}{111}\right)\)
\(A=4\left(\frac{1}{3}-\frac{1}{111}\right)\)
\(A=4.\frac{12}{37}\)
\(A=\frac{48}{37}\)
4x(\(\frac{1}{3.7}+...+\frac{1}{107.111}\) )
4(\(\frac{1}{3}-\frac{1}{7}+...+\frac{1}{107}-\frac{1}{111}\))
4(\(\frac{1}{3}-\frac{1}{111}\))
4.\(\frac{12}{37}\)
48/37
\(\frac{1}{3.7}+\frac{1}{7.11}+...+\frac{1}{\left(4x+3\right)\left(4x+7\right)}=\frac{5}{12}\)(x phải khác \(-\frac{3}{4};-\frac{7}{4}\)nhé)
\(\Leftrightarrow\frac{4}{3.7}+\frac{4}{7.11}+...+\frac{4}{\left(4x+3\right)\left(4x+7\right)}=4.\frac{5}{12}\)
\(\Leftrightarrow\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{4x+3}-\frac{1}{4x+7}=\frac{5}{3}\)
\(\Leftrightarrow\frac{1}{3}-\frac{1}{4x+7}=\frac{5}{3}\)
\(\Leftrightarrow\frac{4x+7-3}{3\left(4x+7\right)}=\frac{5\left(4x+7\right)}{3\left(4x+7\right)}\)
\(\Rightarrow4x+7-3=20x+35\)(chỗ này dùng dấu suy ra nhé)
\(\Leftrightarrow4x-20x=35-7+3\)
\(\Leftrightarrow-16x=31\)
\(\Leftrightarrow x=-\frac{31}{16}\)
V...
\(\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+....+\frac{4}{103.107}\)
=\(\frac{1}{3.7}+\frac{1}{7.11}+\frac{1}{11.15}+...+\frac{1}{103.107}\)
=\(\frac{1}{3.107}\)
=\(\frac{1}{321}\)
k mk nha bn
=
câu 1
\(\Leftrightarrow A=\frac{4}{3}-\frac{4}{7}+\frac{4}{7}-\frac{4}{11}+...+\frac{4}{107}-\frac{4}{111}\)
\(\Rightarrow A=4\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{107}-\frac{1}{111}\right)\)
\(\Rightarrow A=4.\left(\frac{1}{3}-\frac{1}{111}\right)\)
\(\Rightarrow A=4.\frac{12}{37}\)
\(\Rightarrow A=\frac{48}{37}\)
phần B làm tương tự
câu 2:
a)\(\Leftrightarrow x+\frac{7}{12}=\frac{15}{18}\)
\(\Rightarrow x=\frac{15}{18}-\frac{7}{12}\)
\(\Rightarrow x=\frac{1}{4}\)
b,c tương tự như câu 1 phần a
Câu 1:
Ta có: A=1/3-1/7+1/7-1/11+....+1/107-1/111
=> A=1/3+(-1/7+1/7)+(-1/11+1/11)+....+(-1/107+1/107)+(-1)/111
=>A=1/3+(-1)/111
=>A=12/37
Ta có B= 6(1/15.18+1/18.21+...+1/87.90)
=> 3B= 6(3/15.18+3/18.21+...+3/87.90)
=> 3B= 6(1/15-1/18+1/18-1/21+....+1/87-1/90)
(Tương tự như câu A) 3B=6[1/15+(-1)/90]
=> 3B= 6.1/18=1/3
=> B= 1/3:3 = 1/9
