Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
![](https://rs.olm.vn/images/avt/0.png?1311)
1. tính nhanh :
a. 2 x 31 x 12 x 4 x 6 x 42 + 8 x 27 x 3
= ( 2 x 12 ) x 31 + ( 4 x 6 ) x 42 + ( 8 x 3 ) x 27
= 24 x 31 + 24 x 42 + 24 x 27
= 24 x ( 31 + 42 + 27 )
= 24 x 100
= 2400
b. 36 x 28 + 36 x 82 + 64 x 69 + 64 x 41
= ( 36 x 28 + 36 x 82 ) + ( 64 x 69 + 64 x 41 )
= 36 x ( 28 + 82 ) + 64 x ( 69 + 41 )
= 36 x 110 + 64 x 110
= 110 x ( 36 + 64 )
= 110 x 100
= 11000
2. tính các tổng sau :
a, 2 + 4 + 6 + ...... + 1998 + 2000
có số số hạng là : ( 2000 - 2 ) : 2 + 1 = 1000 ( số )
tổng dãy số đó là : ( 2000 + 2 ) x ( 1000 : 2 ) = 1001000
b, 5 + 9 + 13 + ... + 1997 + 2001
có số số hạng là : ( 2001 - 5 ) : 4 + 1 = 500 ( số )
tổng dãy số trên là : ( 2001 + 5 ) x ( 500 : 2 ) = 501500
![](https://rs.olm.vn/images/avt/0.png?1311)
Lời giải:
a.
$23+23\times 45+23\times 44=23\times (1+45+44)=23\times 90$
$=23\times (100-10)=23\times 100-23\times 10=2300-230=2070$
b.
$=36\times 280-36\times 79-36$
$=36\times (280-79-1)=36\times (280-80)=36\times 200=7200$
c.
$=72\times 10+72\times 25+72\times 66-72$
$=72\times (10+25+66-1)=72\times 100=7200$
![](https://rs.olm.vn/images/avt/0.png?1311)
`@` `\text {Ans}`
`\downarrow`
`23 + 23 \times 45 + 23 \times 44`
`= 23 \times (1+45 + 44)`
`= 23 \times 90`
`= 2070`
`b)`
`36 \times 280 - 9 \times 79 \times 4 - 36`
`= 36 \times 280 - 9 \times 4 \times 79 - 36`
`= 36 \times 280 - 36 \times 79 - 36`
`= 36 \times (280 - 79 - 1)`
`= 36 \times 200`
`= 7200`
`c)`
`8 \times 9 \times 10 + 6 \times 25 \times 12 + 4 \times 18 \times 66 - 2 \times 36`
`= 2 \times 4 \times 9 \times 10 + 6 \times 2 \times 6 \times 25 + 2 \times 2 \times 18 \times 66 - 2 \times 36`
`= 10 \times 2 \times 36 + 36 \times 2 \times 25 + 36 \times 2 \times 66 - 2 \times 36`
`= 36 \times 2 \times (10 + 25 + 66 - 1)`
`= 72 \times 100`
`= 7200`
_____
`c)`
`439 \times 78 - 38 \times 78 - 78`
`= 78 \times (439 - 38 - 1)`
`= 78 \times 400`
`= 31200`
`d)`
`24 \times 13 + 6 \times 89 \times 4 - 2 \times 24`
`= 24 \times 13 + 24 \times 89 - 2 \times 24`
`= 24 \times (13 + 89 - 2)`
`= 24 \times 100`
`= 2400`
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(\frac{3}{5}+\frac{2}{5}\right)+\left(\frac{6}{11}+\frac{16}{11}\right)+\left(\frac{7}{13}+\frac{19}{13}\right)\)
= 1 + 2 + 2
= 5
\(=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}\)
= \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)
=\(1-\frac{1}{7}\)
=\(\frac{6}{7}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{42}+\frac{1}{30}+\frac{1}{20}+\frac{1}{12}+\frac{1}{6}+\frac{1}{2}=\frac{1}{1\times2}+\frac{1}{2\times3}+....+\frac{1}{6\times7}=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-...-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)= 1 - 1/7 = 6/7
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a,=\frac{7-1}{1.3.7}+\frac{9-3}{3.7.9}+\frac{13-7}{7.9.13}+\frac{15-9}{9.13.15}\)\(+\frac{19-13}{13.15.19}\)
\(=\frac{1}{1.3}-\frac{1}{3.7}+\frac{1}{3.7}-\frac{1}{7.9}+\frac{1}{7.9}-\frac{1}{9.13}+\frac{1}{9.13}-\frac{1}{13.15}+\frac{1}{13.15}-\frac{1}{15.19}\)
\(=\frac{1}{1.3}-\frac{1}{15.19}=\frac{95}{285}-\frac{1}{285}=\frac{94}{285}\)
\(b,=\frac{1}{6}.\left(\frac{6}{1.3.7}+\frac{6}{3.7.9}+\frac{6}{7.9.13}+\frac{6}{9.13.15}+\frac{6}{13.15.19}\right)\)
làm giống như trên
\(c,=\frac{1}{8}.\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{48.49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{48.49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+...+\frac{50-48}{48.49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{48.49}-\frac{1}{49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{1}{2}-\frac{1}{2450}\right)=\frac{1}{16}.\left(\frac{1225}{2450}-\frac{1}{2450}\right)=\frac{153}{4900}\)
\(d,=\frac{5}{7}.\left(\frac{7}{1.5.8}+\frac{7}{5.8.12}+\frac{7}{8.12.15}+...+\frac{7}{33.36.40}\right)\)
\(=\frac{5}{7}.\left(\frac{8-1}{1.5.8}+\frac{12-5}{5.8.12}+\frac{15-8}{8.12.15}+...+\frac{40-33}{33.36.40}\right)\)
\(=\frac{5}{7}.\left(\frac{1}{1.5}-\frac{1}{5.8}+\frac{1}{5.8}-\frac{1}{8.12}+\frac{1}{8.12}-\frac{1}{12.15}+...+\frac{1}{33.36}-\frac{1}{36.40}\right)\)
\(=\frac{5}{7}.\left(\frac{1}{5}-\frac{1}{1440}\right)=\frac{5}{7}.\left(\frac{288}{1440}-\frac{1}{1440}\right)=\frac{41}{288}\)
P/S: . là nhân nha
a , 38 , 6 + 42 , 78 × 1 , 6 : 0 , 001 = 38 , 6 + 42 , 78 × 1600 = 38 , 6 + 68448 = 68486 , 6 b , 4 , 36 + 13 , 734 : 13 , 08 − 1 , 82 = 4 , 36 − 1 , 82 + 1 , 05 = 2 , 54 + 1 , 05 = 3 , 59