so sanh 3^205+28/3^203+2 và 3^204+19/3^202+1
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so sanh M va N biet M= 3^205+28/3^203+2 N=3^204+19/3^202+1
M = \(\frac{3^{205}+28}{3^{203}+2};\) N = \(\frac{3^{204}+19}{3^{202}+1}\)
So sanh M và N
so sánh
M= 3^205+28/3^203+2
N= 3^204+19/3^202+1
M = \(\dfrac{3^{205}+28}{3^{203}+2};\dfrac{ }{ }\) N = \(\dfrac{3^{204}+28}{3^{202}+1}\)
So sanh M và N
So sánh A và B
A=3205 + 28/ 3203 + 2
B= 3204 +19/ 3202 +1
a,A=45n+245 +n2 (n \(\in\) N*) Chứng tỏ rằng A không chia hết cho 10
b,So sánh M và N biết
M=\(\frac{3^{205}+28}{3^{203}+2}\); N=\(\frac{3^{204}+19}{3^{202}+1}\)
\(\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+.......+\frac{1}{205}}{\frac{204}{1}+\frac{203}{2}+\frac{202}{3}+....+\frac{1}{204}}\)
\(\)Đặt \(A=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}...+\frac{1}{205}}{\frac{204}{1}+\frac{203}{2}+\frac{202}{3}+...+\frac{1}{204}}=\frac{B}{C}\)
Biến đổi C:
\(C=\left(\frac{204}{1}+1\right)+\left(\frac{203}{2}+1\right)+\left(\frac{202}{3}+1\right)+...+\left(\frac{1}{204}+1\right)-204\)
\(=205+\frac{205}{2}+\frac{205}{3}+..+\frac{205}{204}+\frac{205}{205}-205\)
\(=205.\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{205}\right)\)
\(\Rightarrow A=\frac{\frac{1}{2}+\frac{1}{3}+...+\frac{1}{205}}{205.\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{205}\right)}=\frac{1}{205}\)
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Tính nhanh B=\(\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{205}}{\frac{204}{1}+\frac{203}{2}+\frac{202}{3}+...+\frac{1}{204}}\)
So sánh 2 biểu thức sau:
a)A = 10^8+2/10^8-1 và B = 10^8/10^8-3
b)C=17^203+1/17^204+1 và D = 17^202+1/17^203+1
\(A=\frac{10^8+2}{10^8-1}=\frac{10^8-1+3}{10^8-1}=1+\frac{3}{10^8-1}\)
\(B=\frac{10^8}{10^8-3}=\frac{10^8-3+3}{10^8-3}=1+\frac{3}{10^8-3}\)
Nhận thầy 108 - 1 > 108 - 3
=> \(\frac{3}{10^8-1}< \frac{3}{10^8-3}\)
=> \(1+\frac{3}{10^8-1}< \frac{3}{10^8-3}+1\)
=> A < B
b) 17C = \(\frac{17\left(17^{203}+1\right)}{17^{204}+1}=\frac{17^{204}+1+16}{17^{204}+1}=1+\frac{16}{17^{204}+1}\)
17D = \(\frac{17\left(17^{202}+1\right)}{17^{203}+1}=\frac{17^{203}+1+16}{17^{203}+1}=1+\frac{16}{17^{203}+1}\)
Nhận thầy 17203 + 1 < 17204 + 1
=> \(\frac{16}{17^{203}+1}>\frac{16}{17^{204}+1}\)
=> \(\frac{16}{17^{203}+1}+1>\frac{16}{17^{204}+1}+1\Rightarrow17C>17D\Rightarrow C>D\)