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Khong dau nha ban!Minh chi can co gang thi tot ma thoi!dattebayo!
Chúc bạn thi tốt nha dattebayo!
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\(10101\times\left(\frac{5}{111111}+\frac{5}{222222}-\frac{4}{111111}\right)=10101\times\frac{5}{111111}+10101\times\frac{5}{222222}-10101\times\frac{4}{111111}\) \(=\frac{5}{11}+\frac{5}{22}-\frac{4}{11}=\frac{7}{22}\)
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o a b c
Vì trên cùng một nửa mặt phẳng bờ chứa tia oa có góc aoc > góc aob ( 110o> 45o)
\(\Rightarrow\) Tia ob nằm giữa hai tia oc và ob
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\(\dfrac{200-\left(3+\dfrac{2}{3}+\dfrac{2}{4}+\dfrac{2}{5}+...+\dfrac{2}{100}\right)}{\dfrac{1}{2}+\dfrac{2}{3}+\dfrac{3}{4}+...+\dfrac{99}{100}}\\ =\dfrac{200-\left(2+1+\dfrac{2}{3}+\dfrac{2}{4}+\dfrac{2}{5}+...+\dfrac{2}{100}\right)}{\left(1-\dfrac{1}{2}\right)+\left(1-\dfrac{1}{3}\right)+\left(1-\dfrac{1}{4}\right)+...+\left(1-\dfrac{99}{100}\right)}\\ =\dfrac{200-2-1-\dfrac{2}{3}-\dfrac{2}{4}-\dfrac{2}{5}-...-\dfrac{2}{100}}{\left(1+1+1+...+1\right)-\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{100}\right)}\\ =\dfrac{198-\left(\dfrac{2}{2}+\dfrac{2}{3}+\dfrac{2}{4}+\dfrac{2}{5}+...+\dfrac{2}{100}\right)}{99-\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{100}\right)}\\ =\dfrac{2\cdot99-2\cdot\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{100}\right)}{99-\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{100}\right)}\\ =\dfrac{2\cdot\left[99-\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{100}\right)\right]}{99-\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{100}\right)}\\ =2\)
Đề nhỏ quá!! mà t 4 mắt. cẩn thận
Đặt :
\(A=\dfrac{200-\left(3+\dfrac{2}{3}+\dfrac{2}{4}+\dfrac{2}{5}+.............+\dfrac{2}{100}\right)}{\dfrac{1}{2}+\dfrac{2}{3}+\dfrac{3}{4}+....................+\dfrac{99}{100}}\)
\(A=\dfrac{200-2-\left(\dfrac{2}{2}+\dfrac{2}{3}+\dfrac{2}{4}+..............+\dfrac{2}{100}\right)}{1-\dfrac{1}{2}+1-\dfrac{1}{3}+.................+1-\dfrac{1}{100}}\)
\(A=\dfrac{198-\left(\dfrac{2}{2}+\dfrac{2}{3}+..................+\dfrac{2}{100}\right)}{\left(1+1+.....+1\right)-\left(\dfrac{1}{2}+\dfrac{1}{3}+...........+\dfrac{1}{100}\right)}\)
\(A=\dfrac{2\left[99-\left(\dfrac{1}{2}+\dfrac{1}{3}+.............+\dfrac{1}{100}\right)\right]}{99-\left(\dfrac{1}{2}+\dfrac{1}{3}+..............+\dfrac{1}{100}\right)}\)
\(A=2\)
Vậy \(\dfrac{200-\left(3+\dfrac{2}{3}+\dfrac{2}{4}+............+\dfrac{2}{100}\right)}{\dfrac{1}{2}+\dfrac{2}{3}+\dfrac{3}{4}+...............+\dfrac{99}{100}}=2\rightarrowđpcm\)
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ta có : \(6^{100}-1\)
\(\Rightarrow\overline{\left(...6\right)-1}\)
\(=\overline{\left(...5\right)}\)
Vì chữ số tận cùng là 0 hoặc 5 đều chia hết cho 5 . \(\overline{\left(...5\right)}⋮5\)
Vậy : \(6^{100}-1⋮5\)
Ta thấy 6n có chữ số tận cùng là 6
=> 6100 có chữ số tận cùng là 6
=> 6100 - 1 = ......6 - 1 = ......5
Vì ......5 chia hết cho 5 => 6100 - 1 chia hết cho 5 ( đpcm )
= = gian lận![limdim limdim](/media/cke24/plugins/smiley/images/limdim.png)
có ai k giúp tớ vs mai thi r