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Ta có : S = 1.2 + 2.3 + 3.4 + ..... + 32.33
=> 3S = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ...... + 32.33.34
=> 3S = 32.33.34
=> S = \(\frac{32.33.34}{3}=11968\)
Cho A=1/1.2 + 1/2.3 + + 1/ 3.4+...+1/49.50 ; B = 1.2+2.3+3.4+4.5+5.6+...+49.50
Tính 50 mủ 2 A – B/17
\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)
\(=\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{50-49}{49.50}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)
\(=1-\frac{1}{50}=\frac{49}{50}\)
\(B=1.2+2.3+3.4+...+49.50\)
\(3B=1.2.3+2.3.3+3.4.3+...+49.50.3\)
\(=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+49.50.\left(51-48\right)\)
\(=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+49.50.51-48.49.50\)
\(=49.50.51\)
\(B=\frac{49.50.51}{3}=49.50.17\)
\(50^2.A-\frac{B}{17}=49.50-49.50=0\)
Mình làm mẫu 1 bài nha !
Có : 12A = 1.5.12+5.9.12+....+101.105.12
= 1.5.12+5.9.(13-1)+.....+101.105.(109-97)
= 1.5.12+5.9.13-1.5.9+.....+101.105.109-97.101.105
= 1.5.12-1.5.9+101.105.109
= 1155960
=> A = 1155960 : 12 = 96330
Tk mk nha
Có : 4D = 1.2.3.4+2.3.4.4+....+98.99.100.4
= 1.2.3.4+2.3.4.(5-1)+.....+98.99.100.(101-97)
= 1.2.3.4+2.3.4.5-1.2.3.4+......+98.99.100.101-97.98.99.100
= 98.99.100.101
=> D = 98.99.100.101/4 = 24497550
Số các số hạng của A là :
( 99 - 1 ) : 1 + 1 = 99 ( số )
Tổng A là :
( 99 + 1 ) . 99 : 2 = 4950
Vậy tổng A = 4950 .
Dặt A =1.2+3.4+.....+99.100
=>3A=1.2.3+2.3.3+3.4.3+....+99.100.3
=>3A=1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+...99.100(101-98
=>3A=1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 +.....+99.100.101 - 98.99.100
=>3A= 99.100.101
=>A=99.100.101:3
=>A= (99:3).100.101
=>A=33.100.101
=> A=333 300
A=1×2+2×3+3×4+.....+99×100
\(\Leftrightarrow\)3A=1×2×3+2×3×3+3×4×3+....+99×100×3
\(\Leftrightarrow\)3A=1×2×3+2×3×(4-1)+....+99×100×(101-98)
\(\Leftrightarrow\)3A=1×2×3+2×3×4-1×2×3+.....+99×100×101-98×99×100
\(\Leftrightarrow\)3A=99×100×101
\(\Leftrightarrow\)A=\(\frac{99×100×101}{3}\)=33×100×101=333300
3A = 3 . 1 . 2 + 2. 3 .3 + 3 . 4.3 + ... + 59 . 60 . 3
=> 3A = 1.2.( 3 - 0) + 2 . 3.( 4-1) + ...+ 59 .60 . (61 - 58)
=> 3A = 1 . 2 . 3 + 2 . 3.4 - 1.2.3 + 3.4.5 - 2. 3. 4 + ... + 59 . 60 . 61 - 58 . 59 . 60
=> 3A = 59 . 60 . 61
=> A = 71980
A = 1.2+2.3+3.4+.........................+1999.2000
=> 3A= 1.2.(3-0) + 2.3.(4-1) + ... + 1999.2000(2001-1998)
=> 3A=1.2.3+2.3.4-1.2.3+...+1999.2000.2001-1998.1999.2000
=> 3A=1999.2000.2001
A=1999.2000.2001:3=2666666000
=> 3A = 1.2.3 + 2.3.3 + 3.4.3 + ...+ 123.124.3
3A = 1.2.(3 - 0) + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 123.124.(125 - 122)
3A = 1.2.3 - 1.2.0 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ...+ 123.124.125 - 122.123.124
3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ...+ 123.124.125 - 122.123.124
3A = 123.124.125
=> A = \(\frac{123.124.125}{3}=635500\)
A = 1.2 + 2.3 + ........+49.50
3A = 1.2.(3-0) + 2.3.(4-1)+........+49.50.(51 - 48)
3A = 1.2.3 + 2.3.4 - 1.2.3 +........ + 49.50.51 - 48.49.50
3A = 48.49.50 = 117600
A = 39200
Ta có :
Gọi A=1.2+2.3+3.4+4.5+...+49.50
A=1.2+2.3+3.4+4.5+...+49.50
3.A=3.(1.2+2.3+3.4+4.5+...+49.50)
3.A=1.2.3+2.3.3+3.3.4+3.4.5+...+3.49.50
3.A=1.2.(3-0)+2.3.(3-0)+(3-0).3.4+(3-0).4.5+...+(3-0).49.50
3.A=1.2.3-0+2.3.3-0+3.3.4-0+3.4.5-0+...+3.49.50-0
3.A=1.2.3-0+2.3.4-1.2.3+5.3.4-2.3.4+...+49.50.51-48.49.50
3.A=49.50.51
A= 49.50.51/3
A= 49.50.17.3/3
A=49.50.17
A=41650
Đáp số : A=41650
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