1+25=?
25+25+25=?
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25^28+25^24+25^20+...+25^4+1/25^30+25^28+25^26+...+25^2+1
12 tháng 3 2021 lúc 22:51
Rút gọn phân số A = \(\dfrac{25^{28}+25^{24}+25^{20}+...+25^4+1}{25^{30}+25^{28}+....+25^2+1}\)
Lời giải:
Xét tử số:
$\text{TS}=1+25^4+25^8+...+25^{28}$
$25^4.\text{TS}=25^4+25^8+...+25^{32}$
$\Rightarrow \text{TS}(25^4-1)=25^{32}-1$
$\text{TS}=\frac{25^{32}-1}{25^4-1}$
Xét mẫu số:
$\text{MS}=1+25^2+..+25^{30}$
$25^2.\text{MS}=25^2+25^4+...+25^{32}$
$\Rightarrow \text{MS}(25^2-1)=25^{32}-1$
$\Rightarrow \text{MS}=\frac{25^{32}-1}{25^2-1}$
Do đó:
$A=\frac{25^{32}-1}{25^4-1}:\frac{25^{32}-1}{25^2-1}=\frac{25^2-1}{25^4-1}$
$=\frac{25^2-1}{(25^2-1)(25^2+1)}=\frac{1}{25^2+1}$
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Rút gọn \(\frac{25^{28}+25^{24}+25^{20}+...+25^4+1}{25^{30}+25^{28}+25^{26}+...+25^4+25^2+1}\)
\(\dfrac{1}{25}+\dfrac{2}{25}+\dfrac{3}{25}+\dfrac{4}{25}+\dfrac{6}{25}+\dfrac{7}{25}+\dfrac{8}{25}+\dfrac{9}{25}+\dfrac{10}{25}\)
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Tính
\(A=\frac{25^{28}+25^{24}+25^{20}+...+25^4+1}{25^{30}+25^{28}+25^{26}+...+25^2+1}\)
\(A=\frac{25^{28}+25^{24}+25^{20}+...+25^4+1}{25^{30}+25^{28}+25^{26}+...+25^2+1}\)
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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Bài 1:Rút gọn ps
1+25^4+25^5+...+25^28/1+25^2+25^3+...+25^30
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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