3/7x8 | + | 3/8x9 | + ... | 3/63x64 | = | |
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= 1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/7-1/8+1/8-1/9
=1/2-1/9
= 7/18
Dặt \(A=\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{2019.2020}\)
\(A=\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{2019}-\frac{1}{2020}\)
\(A=\frac{1}{6}-\frac{1}{2020}\)
\(A=\frac{1007}{6060}\)
hok tốt!!
1/2x3 +1/3x4 +1/4x5 +1/5x6 + 1/6x7 +1/7x8 + 1/8x9 = 7/18
1/1x2+1/2x3+1/3x4+..+1/9x10
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5+...-1/10
=1-1/10
=9/10
Bài làm:
\(\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{9.10}\)
\(=2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)\)
\(=2\left(\frac{3-2}{2.3}+\frac{4-3}{3.4}+\frac{5-4}{4.5}+...+\frac{10-9}{9.10}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{10}\right)=2.\frac{4}{10}=\frac{4}{5}\)
GỌi dãy tính là A
3A = 6 x 7 x 3 + 7 x 8 x 3 + ... + 21x22x3
3A = 6x7x8 - 5x6x7 + 7x8x9-6x7x8 + ... + 21x22x23 - 20x21x22
3A = 21x22x23 - 5x6x7
3A = 10416
A = 3472
Gọi dãy tính là A
3A = 6 * 7 * 3 + 7 * 8 * 3 + ... + 21 * 22 * 3
3A = 6 * 7 * 8 - 5 *6 *7 + 7 * 8 * 9 - 6 * 7 * 8 + ... + 21 * 22 * 23 - 20 * 21 * 22
3A = 21 * 22 * 23 - 5 * 6 * 7
3A = 10461
A = 3472
Bài làm
Ta có : \(9⋮3\)
nên B = \(\left(5x6x7x8x9\right)⋮3\)
b1
a) \(\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+\dfrac{1}{9.10}\)
\(=\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\)
\(=\dfrac{1}{5}-\dfrac{1}{10}\)
\(=\dfrac{2}{10}-\dfrac{1}{10}\)
\(=\dfrac{1}{10}\)
b) \(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{99.100}\)
\(=\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}\)
\(=\dfrac{1}{1}-\dfrac{1}{100}\)
\(=\dfrac{99}{100}\)
c) \(\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{9.11}\)
\(=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}\)
\(=\dfrac{1}{3}-\dfrac{1}{11}\)
\(=\dfrac{8}{33}\)
d) \(\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{99.101}\)
\(=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{99}-\dfrac{1}{101}\)
\(=\dfrac{1}{3}-\dfrac{1}{101}\)
\(=\dfrac{98}{303}\)