Bài 1: Tính tổng:\(S=\frac{3}{2\cdot3}+\frac{3}{3\cdot6}+\frac{3}{4\cdot9}+\frac{3}{2014\cdot6039}\)
Bài 2: Rút gọn phân số: \(S=\frac{25^{28}+25^{24}+...+25^4+1}{25^{30}+25^{28}+...+25^2+1}\)
Những câu hỏi liên quan
Bài 1: Tính tổng: \(S=\frac{3}{2\cdot3}+\frac{3}{3\cdot6}+\frac{3}{4\cdot9}+...+\frac{3}{6039\cdot2014}\)
Bài 2: Rút gọn phân số: \(S=\frac{25^{28}+25^{24}+...+25^4+1}{25^{30}+25^{28}+...+25^2+1}\)
Rút gọn phân số sau: a)\(\frac{5^2.6^{11}.16^2+6^2.12^6.15^2}{2.6^{12}.10^4-81^2.960^3}\)
\(\frac{25^{28}+25^{24}+...+25^4+1}{25^{30}+25^{28}+...+25^2+1}\)
a)\(\frac{5^{2.}6^{11}.16^2.6^2.12^6.15^2}{2.6^{12}.10^4-81^2.960^3}\)
b)\(\frac{25^{28}+25^{24}+...+25^4+1}{25^{30}+25^{28}+...+25^2+1}\)
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Rút gọn phân số sau: \(\frac{25^{28}+25^{24}+...+25^4+1}{25^{30}+25^{28}+..+25^2+1}\)
Đặt phân số trên là A
\(A=\frac{25^{28}+25^{24}+...+25^4+25^0}{\left(25^{28}+25^{24}+...+25^4+25^0\right)+\left(25^{30}+25^{26}+...+25^6+25^2\right)}\)
\(\frac{1}{A}=\frac{\left(25^{28}+25^{24}+...+25^4+25^0\right)+\left(25^{30}+25^{26}+...+25^6+25^2\right)}{25^{28}+25^{24}+...+25^4+25^0}\)
\(\frac{1}{A}=1+\frac{25^{30}+25^{26}+...+25^6+25^2}{25^{28}+25^{24}+...+25^4+25^0}\)
Đặt \(B=\frac{25^{30}+25^{26}+...+25^6+25^2}{25^{28}+25^{24}+...+25^4+25^0}\)
\(\frac{B}{25^2}=\frac{25^{30}+25^{26}+...+25^6+25^2}{25^{30}+25^{26}+...+25^6+25^2}=1\Rightarrow B=25^2\)
=> \(\frac{1}{A}=1+B=1+25^2\Rightarrow A=\frac{1}{1+25^2}\)
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rút gọn phân số
a, \(\frac{25^{28}+25^{24}+...+25^4+1}{25^{30}+25^{28}+...+25^2+1}\)
1.rút gọn phân số
\(\frac{25^{28}+25^{24}+25^{20}+...+25^4+1}{25^{30}+25^{28}+25^{26}+...25^2+1}\)
2 tháng 2 2021 lúc 12:48
a)Rút gọn phân số : \(\dfrac{25^{28}+25^{24}+25^{20}+.....+25^4+1}{25^{30}+25^{28}+....+25^2+1}\)
b) Cho S = 1-3 + 32-33+.....+398-399
a) Ta có: \(\dfrac{25^{28}+25^{24}+25^{20}+...+25^4+1}{25^{30}+25^{28}+...+25^2+1}\)
\(=\dfrac{25^{24}\left(25^4+1\right)+25^{16}\left(25^4+1\right)+...+\left(25^4+1\right)}{25^{28}\left(25^2+1\right)+25^{24}\left(25^2+1\right)+...+\left(25^2+1\right)}\)
\(=\dfrac{\left(25^4+1\right)\left(25^{24}+25^{16}+25^8+1\right)}{\left(25^2+1\right)\left(25^{28}+25^{24}+...+1\right)}\)
\(=\dfrac{\left(25^4+1\right)\cdot\left[25^{16}\left(25^8+1\right)+\left(25^8+1\right)\right]}{\left(25^2+1\right)\left[25^{24}\left(25^4+1\right)+25^{16}\left(25^4+1\right)+25^8\left(25^4+1\right)+\left(25^4+1\right)\right]}\)
\(=\dfrac{\left(25^4+1\right)\left(25^8+1\right)\left(25^{16}+1\right)}{\left(25^2+1\right)\left(25^4+1\right)\left(25^{24}+25^{16}+25^8+1\right)}\)
\(=\dfrac{\left(25^8+1\right)\left(25^{16}+1\right)}{\left(25^2+1\right)\left[25^{16}\left(25^8+1\right)+\left(25^8+1\right)\right]}\)
\(=\dfrac{\left(25^8+1\right)\left(25^{16}+1\right)}{\left(25^2+1\right)\left(25^8+1\right)\left(25^{16}+1\right)}\)
\(=\dfrac{1}{25^2+1}=\dfrac{1}{626}\)
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Rút gọn phân số : \(A=\frac{25^{28}+25^{24}+25^{20}+....+25^4+1}{25^{30}+25^{28}+25^{26}+....+25^2+1}\)
\(A=\frac{25^{28}+25^{24}+25^{20}+...+25^4+1}{25^{30}+25^{28}+25^{26}+...+25^2+1}=25^{30}+25^{26}+25^{22}+25^{18}+25^{14}+25^{10}+25^6+25^2\)
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Rút gọn \(\frac{25^{28}+25^{24}+25^{20}+...+25^4+1}{25^{30}+25^{28}+25^{26}+...+25^4+25^2+1}\)