- Tìm số tự nhiên n biết: 1+1/3+1/6+...+2/n{n+1}=2007/1004
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LT
1
Những câu hỏi liên quan
31 tháng 10 2017
BAI 1
ta co n+6 chia het cho n
ma n chia het cho n
suy ra 6 chia het cho n
ma n la mot so tu nhien nen
ta co n thuoc U(6)=1,2,3,6
vay n bang 1,2,3,6
bai 2
(2n-1).(y+3)=12
suy ra 2n-1 va y+3 thuoc uoc cua 12 =1,12,3,4,6,2
neu 2n-1 =1 suy ra n=1
thi y+3=12 suy ra y=9
neu 2n-1=12 suy ra n=11/2(ko thoa man )
neu 2n-1=3 suy ra n=2
thi y+3=4 suy ra y=1
neu 2n-1=4 ruy ra n=5/2( ko thoa man )
neu 2n-1=6 suy ra n=7/2( ko thoa man )
neu 2n-1=2 suy ra n=3/2 ( ko thoa man )
vay cac cap so n :y can tim la (2;1),(1;9)
NH
1
15 tháng 12 2017
1/3 + 1/6 + 1/10 + ... + 2/n(n+1) = 2003/2004
\(\Rightarrow\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{n.\left(n+1\right)}=\frac{2003}{4008}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{n}-\frac{1}{n+1}=\frac{2003}{4008}\)
\(\Rightarrow\frac{1}{2}-\frac{1}{n+1}=\frac{2003}{4008}\)
\(\Rightarrow\frac{1}{n+1}=\frac{1}{2}-\frac{2003}{4008}\)
\(\Rightarrow\frac{1}{n+1}=\frac{1}{4008}\)
\(\Rightarrow n+1=4008\)
\(\Rightarrow n=4008-1=4007\)
HM
1
27 tháng 1 2017
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{n\left(n+1\right)}=\frac{2003}{2004}\)
\(\Leftrightarrow\frac{1}{2}\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+....+\frac{2}{n\left(n+1\right)}\right)=\frac{1}{2}.\frac{2003}{2004}\)
\(\Leftrightarrow\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{n\left(n+1\right)}=\frac{2003}{4008}\)
\(\Leftrightarrow\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{n\left(n+1\right)}=\frac{2003}{4008}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{n}-\frac{1}{n+1}=\frac{2003}{4008}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{n+1}=\frac{2003}{4008}\)
\(\Leftrightarrow\frac{1}{n+1}=\frac{1}{2}-\frac{2003}{4008}=\frac{1}{4008}\)
\(\Rightarrow n+1=4008\Rightarrow n=4007\)
Vậy \(n=4007\)
NT
1
6 tháng 1 2021
TÍnh S=3/1.4+3/4.7+3?7>!0+...+3/n(n+3) với n là số tự nhiên . chứng minh S<1
C
0
ZV
3
NN
Nguyễn Ngọc Anh Minh
CTVHS
VIP
12 tháng 5 2016
Đặt vế trái là A ta có:
\(\frac{A}{2}=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\)
\(\frac{A}{2}=\frac{3-2}{2.3}+\frac{4-3}{3.4}+\frac{5-4}{4.5}+...+\frac{x+1-x}{x\left(x+1\right)}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}\)
\(\frac{A}{2}=\frac{1}{2}-\frac{1}{x+1}\Rightarrow\frac{A}{2}=\frac{x+1-2}{2\left(x+1\right)}\Rightarrow A=\frac{x-1}{x+1}\)
\(\Rightarrow\frac{x-1}{x+1}=\frac{2007}{2009}\Leftrightarrow x=2003\)
29 tháng 11 2022
\(\frac{A}{2}=\frac{1}{2}-\frac{1}{x+1}\Rightarrow\frac{A}{2}=\frac{x+1-2}{2\left(x+1\right)}\Rightarrow...
1+1/3+1/6+...+2/n(n+1)=2007/1004
=>2/1.2+2/6+2/12+...+2/n(n+1)
=>2/1.2+2/2.3+2/3.4+...+2/n(n+1)
=>2[1/1.2+1/2.3+1/3.4+...+1/n(n+1)]=2007/1004
=>2[1/1-1/2+1/2-1/3+1/3-1/4+...+1/n-1/n+1]=2007/1004
=>2[1/1-1/n+1]=2007/1004
=>1/1-1/n+1=2007/2008
=>1/n+1=1/2008
=>n+1=2008
=>n=2007