\(\frac{1}{2\times3}\)+\(\frac{1}{3\times4}\)+. . .+\(\frac{1}{a\times\left(a+1\right)}\)=\(\frac{49}{100}\)
Tìm a
Tìm số tự nhiên biết : \(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{a\times\left(a+1\right)}=\frac{49}{100}\)
Trả lời : a =................
\(\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{a\times\left(a+1\right)}=\frac{49}{100}\)
\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{a}-\frac{1}{\left(a+1\right)}=\frac{49}{100}\)
\(\frac{1}{2}-\frac{1}{a+1}=\frac{49}{100}\)
\(\frac{50}{100}-\frac{1}{a+1}=\frac{49}{100}\)
\(\frac{1}{a+1}=\frac{50}{100}-\frac{49}{100}\)
\(\frac{1}{a+1}=\frac{1}{100}\)
\(\Rightarrow a+1=100\)
\(\Rightarrow a=100-1\)
\(a=99\)
Số a chính là: 99
Chúc bạn may mắn......mình chính là Đào Minh Tiến!
tính \(A=\frac{1}{2}\times\left(1+\frac{1}{1\times3}\right)\times\left(1+\frac{1}{2\times4}\right)\times\left(1+\frac{1}{3\times5}\right)\times...\times\left(1+\frac{1}{2015\times2017}\right)\)
\(A=\frac{1}{2}\left(1+\frac{1}{1\cdot3}\right)\left(1+\frac{1}{2\cdot4}\right)...\left(1+\frac{1}{2015\cdot2017}\right)\)\(A=\frac{1}{2}\left(\frac{1\cdot3+1}{1\cdot3}\right)\left(\frac{2\cdot4+1}{2\cdot4}\right)...\left(\frac{2015\cdot2017+1}{2015\cdot2017}\right)\)
\(A=\frac{1^2}{2}\cdot\frac{2^2}{1\cdot3}\cdot\frac{3^2}{2\cdot4}\cdot\cdot\cdot\frac{2016^2}{2015\cdot2017}\)
\(A=\frac{1^2\cdot2^2\cdot3^2\cdot\cdot\cdot2016^2}{2\cdot1\cdot3\cdot2\cdot4\cdot\cdot\cdot2015\cdot2017}\)
\(A=\frac{2016}{2017}\)
A = \(\left(1+\frac{1}{1\times3}\right)\times\left(1+\frac{1}{2\times4}\right)\times\left(1+\frac{1}{3\times5}\right)\times....\times\left(1+\frac{1}{5\times7}\right)\)=?
1=3/3=4/4=5/5=...
=> 1+1/1*3=3/1*3=1/1
=> 1+1/2*4=4/2*4=1/2
=>...
Bieu thuc se con lai la 1*1/2*1/3*1/4*1/5
Vay A=1/120
\(A=\left[1-\left(\frac{1}{1\times2\times3}+\frac{1}{2\times3\times4}+......+\frac{1}{98\times99\times100}\right)\right]\times\frac{14851}{19800}\)
a,A=\(\frac{1}{2}-\frac{1}{2^2}+\frac{1}{2^3}-\frac{1}{2^4}+...+\frac{1}{2^{99}}-\frac{1}{2^{100}}\)
b,B=\(\frac{1}{1\times2\times3}+\frac{1}{2\times3\times4}+\frac{1}{3\times4\times5}+...+\frac{1}{998\times999\times100}\)
c,C=\(\frac{1+\left(1+2\right)+\left(1+2+3\right)+...+\left(1+2+3+...+98\right)}{1\times98+2\times97+3\times96+...+98\times1}\)
Tính C=\(\frac{1}{1\times2\times3}+\frac{1}{2\times3\times4}+\frac{1}{3\times4\times5}+....+\frac{1}{n\times\left(n+1\right)\times\left(n+2\right)}\)
Bạn nào giúp mik nhớ viết cả cách giải cho mik nhé!!!!!!!!!!
\(1\frac{13}{15}\times3\times\left(0,5\right)^2\times3+\left(\frac{8}{15}-1\frac{19}{60}\div1\frac{23}{24}\right)\)
\(\left(-3,2\right)\times\frac{-15}{64}+\left(0,8-2\frac{4}{15}\right)\div1\frac{23}{24}\)
Bài 2 rút gọn\(\frac{2\times\left(-13\right)\times9\times10}{\left(-3\right)\times4\times\left(-5\right)\times26}\)
\(\frac{15\times8+15\times4}{12\times3}\)
\(1\frac{13}{15}\cdot3\cdot(0,5)^2\cdot3+\left[\frac{8}{15}-1\frac{19}{60}:1\frac{23}{24}\right]\)
\(=\frac{28}{15}\cdot3\cdot0,5\cdot0,5\cdot3+\left[\frac{8}{15}-\frac{79}{60}:\frac{47}{24}\right]\)
\(=\frac{28}{5}\cdot0,25\cdot3+\left[\frac{32}{60}-\frac{79}{60}\cdot\frac{24}{47}\right]\)
\(=\frac{28}{5}\cdot\frac{25}{100}\cdot3+\left[\frac{32}{60}-\frac{158}{235}\right]\)
\(=\frac{28}{5}\cdot\frac{1}{4}\cdot3+\frac{-98}{705}=\frac{7}{5}\cdot1\cdot3+\frac{-98}{705}\)
Đến đây là tính dễ rồi :v
\((-3,2)\cdot\frac{-15}{64}+\left[0,8-2\frac{4}{15}\right]:1\frac{23}{24}\)
\(=\frac{-32}{10}\cdot\frac{-15}{64}+\left[\frac{8}{10}-\frac{34}{15}\right]:\frac{47}{24}\)
\(=\frac{-32\cdot(-15)}{10\cdot64}+\left[\frac{4}{5}-\frac{34}{15}\right]:\frac{47}{24}\)
\(=\frac{-1\cdot(-3)}{2\cdot2}+\frac{4\cdot3-34}{15}:\frac{47}{24}\)
\(=\frac{3}{4}+\frac{-22}{15}:\frac{47}{24}\)
\(=\frac{3}{4}+\frac{-517}{180}=\frac{-191}{90}\)
Bài 2 : \(\frac{2\cdot(-13)\cdot9\cdot10}{(-3)\cdot4\cdot(-5)\cdot26}=\frac{1\cdot(-1)\cdot3\cdot2}{(-1)\cdot2\cdot(-1)\cdot2}=\frac{1\cdot3}{-1\cdot2}=\frac{3}{-2}=\frac{-3}{2}\)
\(\frac{15\cdot8+15\cdot4}{12\cdot3}=\frac{15\cdot(8+4)}{12\cdot3}=\frac{15\cdot12}{12\cdot3}=\frac{15}{3}=5\)
Tinh \(\left(1-\frac{2}{2\times3}\right)\times\left(1-\frac{2}{3\times4}\right)\times\left(1-\frac{2}{4\times5}\right)\times...\times\left(1-\frac{2}{2015\times2016}\right)\)
Tìm x:
\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{x\times\left(x+1\right)}=\frac{2015}{2016}\)
1-1/x+1=2015/2016
=>1/x+1=1-2015/2016=1/2016
=>x+1=2016=>x=2015
mình không ghi lại đề nha:
\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2015}{2016}\)
<=>\(1-\frac{1}{x+1}=\frac{2015}{2016}\)
<=>\(\frac{x}{x+1}=\frac{2015}{2016}\)
=>x=
Đến đó bạn tự giải tiếp ha
=>(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/x-1/x+1)=2015/2016
=>1/1-1/x+1=2015/2016
=>x/x+1=2015/2016
=>x=2015