tinh
1/1.2.3+1/2.3.4+....+1/99.100.101
tinh A=1/1.2.3+1/2.3.4+....+1/99.100.101
\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{99.100.101}\)
\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{99.100}-\frac{1}{100.101}\right)\)
\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{100.101}\right)\)
\(=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{10100}\right)=\frac{5049}{20200}\)
A=1/2(1/1.2-1/2.3+1/2.3-1/3.4+.......+1/99.100-1/100.101)
A=1/2(1/1.2-1/100.101)
A=1/2(1/1.2-1/100.101)=5049/202000
A=1/2(1/1.2-1/2.3+1/2.3-1/3.4+.......+1/99.100-1/100-1/101
A=1/2(1/1.2-1/101)
A=5049/20200
tinh
1/1.2.3+1/2.3.4+.....+1/99.100.101
\(\frac{1}{1.2.3}+\frac{1}{1.2.3}+...+\frac{1}{99.100.101}\)
\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{99.100}-\frac{1}{100.101}\right)\)
\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{100.101}\right)=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{10100}\right)=\frac{5049}{20200}\)
Tính: 1/1.2.3+1/2.3.4+1/3.4.5+...+1/99.100.101
Đặt A=1/1.2.3+1/2.3.4+...+1/99.100.101
2A=2/1.2.3+2/2.3.4+...2/99.100.101
2A=3-1/1.2.3+4-2/2.3.4+...+101-99/99.100.101
2A=3/1.2.3-1/1.2.3+4/2.3.4-2/2.3.4+...+101/99.100.101-99/99.100.101
2A=1/1.2-1/2.3+1/2.3-1/3.4+...+1/99.100-1/100.101
2A=1/2-1/10100
tìm x:
1/1.2.3+1/2.3.4+.....+1/99.100.101=1/x.(1.2-1/99.100)
A = 1/2.3.4 +1/2.3.4.5 + 1/3.4.5.6 + ... +1/47.48.49.50
B= 1/1.2+1/1.2.3 - 1/2.3.4 + 1/.3.4 -1/3.4.5 ... +1/99.100 - 1/99.100.101
Tính
A = \(\frac{1}{1.2.3}-\frac{1}{2.3.4}-.......-\frac{1}{99.100.101}\)
Tính E = 1/1.2-1/1.2.3+1/2.3-1/2.3.4+1/3.4-1/3.4.5+...+1/99.100-1/99.100.101
\(E=\frac{1}{1.2}-\frac{1}{1.2.3}+\frac{1}{2.3}-\frac{1}{2.3.4}+....+\frac{1}{99.100}-\frac{1}{99.100.101}\)
\(=\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\right)-\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{99.100.101}\right)\)
\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}=\frac{99}{100}\)
\(B=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{99.100.101}\)
\(=\frac{1}{2}\left(\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+...+\frac{101-99}{99.100.101}\right)\)
\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{99.100}-\frac{1}{100.101}\right)\)
\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{100.101}\right)=\frac{5049}{20200}\)
Suy ra \(E=A-B=\frac{99}{100}-\frac{5049}{20200}=\frac{14949}{20200}\)
\(\frac{14949}{20200}\)
Tính \(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+.....+\frac{1}{99.100.101}\)
=1+\(\frac{1}{2}\)-\(\frac{1}{3}\)+\(\frac{1}{2}\) -\(\frac{1}{3}\) -\(\frac{1}{4}\)+\(\frac{1}{3}\) - \(\frac{1}{4}\)-\(\frac{1}{5}\)+.....+\(\frac{1}{99}\)-\(\frac{1}{100}\)-\(\frac{1}{101}\)
=1+\(\frac{1}{101}\)
=\(\frac{102}{101}\)
1/1.2.3 = 1/2 .[1/1.2 - 1 / 2.3]
1/2.3.4 = 1/2[ 1/2- 1/3 ]
...................
1/99.100.101 = 1/2[ 1/99. 100 - 1/100.101]
=> A= 1/2 [ 1/1.2- 1/2.3 + 1/2.3 - 1/3.4 + 1/3.4 - 1/ 4.5 +.........+ 1/99 .100 - 1/100. 101]
A = 1/2 . [1/1.2 -1/100 .101]
A= 1/2 . 5049 /10100 = 5049 / 20200.
Mình nghĩ là vậy đó.
A= 1.2.3+2.3.4+.......+99.100.101
Kết quả là : \(\frac{5049}{20200}\)
A = 1.2.3 + 2.3.4 + ... + 99.100.101
=> 4A = 1.2.3.4 + 2.3.4.4 + ... + 99.100.101.4
=> 4A = 1.2.3.4 + 2.3.4.(5 - 1) + ... + 99.100.101.(102 - 98)
=> 4A - 1.2.3.4 + 2.3.4.5 - 1.2.3.4 + ... + 99.100.101.102 - 98.99.100.101
=> 4A = 99.100.101.102
=> A = 99.100.101.102 :4
=> A = 25497450
\(=\frac{5049}{20200}\)
Code : Breacker