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Xét tử:
\(\frac{1}{19}+\frac{2}{18}+\frac{3}{17}+....+\frac{19}{1}\)
= \(\left(1+\frac{1}{19}\right)+\left(1+\frac{2}{18}\right)+\left(1+\frac{3}{17}\right)+.....+\left(1+\frac{18}{2}\right)+1\)
= \(\frac{20}{19}+\frac{20}{18}+\frac{20}{17}+.....+\frac{20}{2}+1\)
= \(\frac{20}{20}+\frac{20}{19}+\frac{20}{18}+\frac{20}{17}+...+\frac{20}{2}\)
= \(20\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{20}\right)\)
Thay vào, ta có:
D = \(\frac{20\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{20}\right)}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{20}}\)
=> D = 20
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* Cách làm : Tử giữ nguyên,còn mẫu ta biến đổi như sau:
Mẫu : ( \(\frac{19}{1}\)+ 1 ) + ( \(\frac{18}{2}\)+ 1 ) + ( \(\frac{17}{3}\)+ 1 ) +...+ ( \(\frac{3}{17}\)+ 1 ) + ( \(\frac{2}{18}\)+ 1 ) + ( \(\frac{1}{19}\)+ 1 ) - 19 ( vì ta cộng với 19 số 1 nên phải trừ 19 )
= \(\frac{20}{1}\)+ \(\frac{20}{2}\)+ \(\frac{20}{3}\)+...+ \(\frac{20}{17}\)+ \(\frac{20}{18}\)+ \(\frac{20}{19}\)- 19
= \(\frac{20}{2}\)+ \(\frac{20}{3}\)+...+ \(\frac{20}{17}\)+ \(\frac{20}{18}\)+ \(\frac{20}{19}\)+ ( \(\frac{20}{1}\)- 19)
= \(\frac{20}{2}\)+ \(\frac{20}{3}\)+ ...+ \(\frac{20}{17}\)+ \(\frac{20}{18}\)+ \(\frac{20}{19}\)+ \(\frac{20}{20}\)
= 20.( \(\frac{1}{2}\)+ \(\frac{1}{3}\)+...+ \(\frac{1}{17}\)+ \(\frac{1}{18}\)+ \(\frac{1}{19}\)+ \(\frac{1}{20}\))
=> \(\frac{Tử}{Mâu}\)= \(\frac{1}{20}\)
Phùng Quang Thịnh biến đổi sai 1 chỗ kìa
-19 = \(\frac{20}{20}-20\)chứ mà bạn
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Bài làm
Có (99-17)+1=83 phần tử
Số ở giữa sẽ là 17+(82/2) = 58
Những số khác tạo thành các cặp
=(17+99) + (18+98)+...+58
=116*(82/2)+58= 4814
so so hang trong tong la : (99-17) :1 +1 = 83
tong la : (99+17) x 83 :2 =4814
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Có \(\frac{18}{18+19+20}>\frac{18}{18+19+20+21}\)
\(\frac{19}{18+19+21}>\frac{19}{18+19+20+21}\)
\(\frac{20}{18+19+21}>\frac{20}{18+19+20+21}\)
\(\frac{21}{18+19+21}>\frac{21}{18+19+20+21}\)
=> \(\frac{18}{18+19+20}+\frac{19}{18+19+21}+\frac{20}{18+19+21}+\frac{21}{18+19+21}>\frac{18}{18+19+20+21}+\frac{19}{18+19+20+21}+\frac{20}{18+19+20+21}+\frac{21}{18+19+20+21}\)
=> \(\frac{18}{18+19+20}+\frac{19}{18+19+21}+\frac{20}{18+19+21}+\frac{21}{18+19+21}>\frac{18+19+20+21}{18+19+20+21}\)
=>\(\frac{18}{18+19+20}+\frac{19}{18+19+21}+\frac{20}{18+19+21}+\frac{21}{18+19+21}>1\)
=>M>1
Còn lại mình không biết, đúng thì tick nha
![](https://rs.olm.vn/images/avt/0.png?1311)
17 (18 + 19) + 12 (18 + 19) - 18 - 19
17.37+12.37-18-19
37.(17+12)-18-19
37.29-18-19
1073-18-19
1066-19
1036
k nhé
.................xoxo................
\(D=\frac{19^{17}\left(1+19\right)}{19^{18}\left(1+19\right)}=\frac{1}{19}\)