17/18-1/16
giải phương trình :
1/(16√17+17√16)+1/(17√18+18√17)+1/(18√19+19√18)+⋯+1/(x√(x+1)+(x+1)√x)=499/2012
chứng minh rằng:\(\frac{17^{18}+1}{17^{19}+1}< \frac{17^{18}+1+16}{17^{19}+1+16}\)
-5 phan14 và 30 phân -84 có bằng nhau không tại sao
Tính:\(\frac{\frac{1}{18}+\frac{2}{17}+\frac{3}{16}+...+\frac{18}{1}+18}{\frac{1}{18}+\frac{1}{17}+\frac{1}{16}+...+1}\)
Tính nhẩm:
a)
15 − 6=..... 15 − 7=.....
15 − 8=..... 15 − 9=.....
16 − 7=..... 16 − 8=.....
16 − 9=..... 17 − 8=.....
17 − 9=..... 18 − 9=.....
b)
18 − 8 − 1=..... 18 − 9=.....
15 − 5 − 2=..... 15 − 7=.....
16 − 6 − 3=..... 16 − 9=.....
Phương pháp giải:
Trừ nhẩm các số rồi điền kết quả vào chỗ trống.
Lời giải chi tiết:
a)
15 − 6 = 9 15 − 7 = 8
15 − 8 = 7 15 − 9 = 6
16 − 7 = 9 16 − 8 = 8
16 − 9 = 7 17 − 8 = 9
17 − 9 = 8 18 − 9 = 9
b)
18 − 8 − 1 = 9 18 − 9 = 9
15 − 5 − 2 = 8 15 − 7 = 8
16 − 6 − 3 = 7 16 − 9 = 7
15 - 6 = 9,
15 - 8 =7,
15 - 7 = 8,
15 - 9 = 6
So sánh :
A= 1618-1 / 1-1617 và
B= 1617-1 / 1-1616
(1/18+2/17+3/16+4/15+5/14+4/13+ ...+18/1+18)/1/18
\(\dfrac{16}{17}:^{1\dfrac{1}{17}}:^{1\dfrac{1}{18}}:^{1\dfrac{1}{19}}\)
\(\dfrac{16}{17}:1\dfrac{1}{17}:1\dfrac{1}{18}:1\dfrac{1}{19}\)
\(=\dfrac{16}{17}:\dfrac{18}{17}:\dfrac{19}{18}:\dfrac{20}{19}=\dfrac{16}{17}.\dfrac{17}{18}.\dfrac{18}{19}.\dfrac{19}{20}=\dfrac{16}{20}=\dfrac{4}{5}\)
M=15/15×16+15/16×17+15/17×18+15/18×19+15/19×20
Ko doi ra so thap phan chung to M<1/3
M = \(15.\left(\frac{1}{15.16}+\frac{1}{16.17}+...+\frac{1}{19.20}\right)\)
= \(15.\left(\frac{1}{15}-\frac{1}{16}+\frac{1}{16}-\frac{1}{17}+...+\frac{1}{19}-\frac{1}{20}\right)\)
= \(15.\left(\frac{1}{15}-\frac{1}{20}\right)\)
= \(15.\frac{1}{60}\)= \(\frac{1}{4}\)\(< \frac{1}{3}\)
(=) \(M< \frac{1}{3}\)\(\left(đpcm\right)\)
Ta có: \(M=\frac{15}{15.16}+\frac{15}{16.17}+\frac{15}{17.18}+\frac{15}{18.19}+\frac{15}{19.20}\)
\(\Rightarrow M=15.\left(\frac{1}{15.16}+\frac{1}{16.17}+\frac{1}{17.18}+\frac{1}{18.19}+\frac{1}{19.20}\right)\)
\(\Rightarrow M=15.\left(\frac{1}{15}-\frac{1}{16}+\frac{1}{16}-\frac{1}{17}+\frac{1}{17}-\frac{1}{18}+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\right)\)
\(\Rightarrow M=15.\left(\frac{1}{15}-\frac{1}{20}\right)\)
\(\Rightarrow M=15.\frac{1}{60}=\frac{1}{4}\)
Ta thấy: \(\frac{1}{4}< \frac{1}{3}\Rightarrow M< \frac{1}{3}\)
Vậy \(M< \frac{1}{3}\)
Chúc bạn học tốt!
\(\Rightarrow M=15.\left(\frac{1}{15.16}+\frac{1}{16.17}+...+\frac{1}{19.20}\right)\)
\(M=15.\left(\frac{1}{15}-\frac{1}{16}+\frac{1}{16}-\frac{1}{17}+...+\frac{1}{19}-\frac{1}{20}\right)\)
\(M=15.\left(\frac{1}{15}+\left(-\frac{1}{16}+\frac{1}{16}\right)+\left(-\frac{1}{17}+\frac{1}{17}\right)+...+\left(\frac{-1}{19}+\frac{1}{19}\right)-\frac{1}{20}\right)\)
\(M=15.\left(\frac{1}{15}+0+0+0+...+0-\frac{1}{20}\right)\)
\(M=15.\left(\frac{1}{15}-\frac{1}{20}\right)=\frac{15}{60}\)
Mà \(\frac{1}{3}=\frac{20}{60}\)
\(\Rightarrow M< \frac{1}{3}\)
Vậy : \(M< \frac{1}{3}\)