Tính nhanh
\(6x7+7x8+8x9+...+20x21+21x22\)
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\(\frac{10}{2\cdot3}+\frac{10}{3\cdot4}+\frac{10}{4\cdot5}+...+\frac{10}{8\cdot9}\)
\(=10\cdot\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}\right)\)
\(=10\cdot\left(\frac{1}{2}-\frac{1}{9}\right)=10\cdot\frac{7}{18}=\frac{35}{9}\)
\(=10\cdot\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}\right)\)
\(=10\cdot\left(\frac{1}{2}-\frac{1}{9}\right)\)
\(=10\cdot\frac{7}{9}\)
\(=\frac{70}{9}\)
\(\dfrac{1}{5\times6}+\dfrac{1}{6\times7}+\dfrac{1}{7\times8}+\dfrac{1}{8\times9}+\dfrac{1}{9\times10}\)
= \(\dfrac{1}{5}-\dfrac{1}{6}\times\dfrac{1}{6}-\dfrac{1}{7}\times\dfrac{1}{7}-\dfrac{1}{8}\times\dfrac{1}{8}-\dfrac{1}{9}\times\dfrac{1}{9}-\dfrac{1}{10}\)
= \(\dfrac{1}{5}-\dfrac{1}{10}\)
= \(\dfrac{1}{10}\)
\(B=\left(\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{50\cdot51}\right)+\left(\dfrac{5}{6}+\dfrac{19}{20}+...+\dfrac{2549}{2550}\right)\)
\(B=\left(\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+..+\dfrac{1}{50\cdot51}\right)+\left(1-\dfrac{1}{2\cdot3}\right)+\left(1-\dfrac{1}{3\cdot4}\right)+...+\left(1-\dfrac{1}{50\cdot51}\right)\)
\(B=\left(1+1+...+1\right)+\left(\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{50\cdot51}\right)-\left(\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{50\cdot51}\right)\)
\(B=1\cdot49=49\) (vì có (50 - 2) : 1 + 1 = 49 số hạng 1)
1 x 2 = 2
5 x 6 = 30
2 x 3 = 6
6 x 7 = 42
3 x 4 = 12
7 x 8 = 56
4 x 5 = 20
8 x 9 = 72
HT
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