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Ta có : \(A=\frac{1}{5^2}+\frac{2}{5^3}+...+\frac{n}{5^{n+1}}+...+\frac{11}{5^{12}}\)
=> \(5A=\frac{1}{5}+\frac{2}{5^2}+...+\frac{n}{5^n}+...+\frac{11}{5^{11}}\)
Lấy 5A trừ A theo vế ta có :
5A - A = \(\left(\frac{1}{5}+\frac{2}{5^2}+...+\frac{n}{5^n}+...+\frac{11}{5^{11}}\right)-\left(\frac{1}{5^2}+\frac{2}{5^3}+...+\frac{n}{5^{n+1}}+...+\frac{11}{5^{12}}\right)\)
4A = \(\left(\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{11}}\right)-\frac{11}{5^{12}}\)
Đặt B = \(\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{11}}\)
=> 5B = \(1+\frac{1}{5}+...+\frac{1}{5^{10}}\)
Lấy 5B trừ B ta có :
=> 5B - B = \(\left(1+\frac{1}{5}+...+\frac{1}{5^{10}}\right)-\left(\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{11}}\right)\)
=> 4B =\(1-\frac{1}{5^{11}}\)
=> B = \(\frac{1}{4}-\frac{1}{5^{11}.4}\)
Khi đó 4A = \(\frac{1}{4}-\frac{1}{5^{11}.4}-\frac{1}{5^{12}}\)
=> A = \(\frac{1}{16}-\left(\frac{1}{5^{11}.16}+\frac{1}{5^{12}.4}\right)< \frac{1}{16}\left(\text{ĐPCM}\right)\)
cậu ơi , mình quên không ghi 1 dữ liệu ạ
n thuộc N
V ậy có cần phải chỉnh sửa ở trong bài làm không ạ?????
a, 11 1/4-(2 5/7+5 1/4)
= 45/4-(19/7+21/4)
= 45/4-223/28
=23/7
b, (8 5/11+3 5/8)-3 5/11
=(93/11+29/8)-38/11
=1063/88-38/11
=69/8
a, =\(11\frac{1}{4}-2\frac{5}{7}-5\frac{1}{4}\)
\(=\left(11\frac{1}{4}-5\frac{1}{4}\right)-2\frac{5}{7}\)
\(=6-2\frac{5}{7}\)
\(=\frac{23}{7}\)
b, \(=8\frac{5}{11}+3\frac{5}{8}-3\frac{5}{11}\)
\(=\left(8\frac{5}{11}-3\frac{5}{11}\right)+3\frac{5}{8}\)
\(=5+3\frac{5}{8}\)
\(=\frac{69}{8}\)
1)
a)
\(\frac{-5}{6}.\frac{120}{25}< x< \frac{-7}{15}.\frac{9}{14}\)
\(\frac{-1}{1}.\frac{20}{5}< x< \frac{-1}{5}.\frac{3}{2}\)
\(\frac{-20}{5}< x< \frac{-3}{10}\)
\(\frac{-40}{10}< x< \frac{-3}{10}\)
\(\Rightarrow Z\in\left\{-4;-5;-6;-7;-8;-9;-10;...;-39\right\}\)
\(a,\frac{5}{7}+\frac{2}{7}:x=\frac{-11}{14}\)
\(\Rightarrow\frac{2}{7}:x=\frac{-11}{14}-\frac{5}{7}\)
\(\Rightarrow\frac{2}{7}:x=\frac{-11}{14}-\frac{10}{14}\)
\(\Rightarrow\frac{2}{7}:x=\frac{-21}{14}\)
\(\Rightarrow\frac{2}{7}:x=\frac{-3}{2}\)
Tự tìm x được rồi :v
\(b,\frac{2}{3}x-\frac{1}{2}x=\frac{5}{12}\)
\(\Rightarrow\left[\frac{2}{3}-\frac{1}{2}\right]x=\frac{5}{12}\)
\(\Rightarrow\left[\frac{4}{6}-\frac{3}{6}\right]x=\frac{5}{12}\)
\(\Rightarrow\frac{1}{6}x=\frac{5}{12}\)
\(\Rightarrow x=\frac{5}{12}:\frac{1}{6}=\frac{5}{12}\cdot\frac{6}{1}=\frac{5}{2}\cdot\frac{1}{1}=\frac{5}{2}\)
\(c,\left[x+\frac{1}{2}\right]^2+\frac{17}{25}=\frac{26}{25}\)
\(\Rightarrow\left[x+\frac{1}{2}\right]^2=\frac{26}{25}-\frac{17}{25}\)
\(\Rightarrow\left[x+\frac{1}{2}\right]^2=\frac{9}{25}\)
\(\Rightarrow x+\frac{1}{2}=\pm\frac{3}{5}\)
\(\Rightarrow\hept{\begin{cases}x+\frac{1}{2}=\frac{3}{5}\\x+\frac{1}{2}=-\frac{3}{5}\end{cases}}\Rightarrow\hept{\begin{cases}x=\frac{1}{10}\\x=-\frac{11}{10}\end{cases}}\)
d, Tự làm
P/S : Thông cảm cho mk nhé vì máy tính mk ko bấm dấu ngoặc tròn được :v
\(-3\frac{3}{5}.x=\frac{4}{15}\)
\(\frac{-18}{5}.x=\frac{4}{15}\)
\(x=\frac{4}{15}:\frac{-18}{5}\)
\(x=\frac{-2}{27}\)