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A.3=5.6.3+6.7.3+...+30.31.3
A.3=5.6.(7-4)+6.7.(8-5)+...+30.31.(32-29)
A.3=5.6.7-4.5.6+6.7.8-5.6.7+...+30.31.32-29.30.31
A.3=(5.6.7-5.6.7)+...+(29.30.31-29.30.31)+(30.31.32-4.5.6)
A.3=0+...+0+30.31.32-4.5.6
A.3=30.31.32-4.5.6
A=30.31.32-4.5.6 /3
A=(29760-120)/3
A=29460/3
A=9880
vậy A là 9880
lưa ý dấu này/ nghĩa là chia
3.A = 5.6.(7-4) + 6.7.(8-5) + ....+30.31.(32- 29)
3.A = 5.6.7 - 4.5.6 + 6.7.8 - 5.6.7 + ...+ 30.31.32 - 29.30.31
3.A = (5.6.7 + 6.7.8 + ...+ 30.31.32) - (4.5.6 + 5.6.7 + ...+ 29.30.31)
3.A = 30.31.32 - 4.5.6 = 29 640 => A = 9 880
A = 1.2.3 + 2.3.4 + 3.4.5 + ... + 20.21.22
4A = 1.2.3.4 + 2.3.4.4 + 3.4.5.4 + ... + 20.21.22.4
4A = 1.2.3.4 + 2.3.4.(5 - 1) + 3.4.5.(6 - 2) + ... + 20.21.22.(23 - 19)
4A = 1.2.3.4 + 2.3.4.5 - 1.2.3.4 + 3.4.5.6 - 2.3.4.5 + ... + 20.21.22.23 - 19.20.21.22
4A = 20.21.22.23
A = 20.21.22.23 : 4
A = 53130
Đặt A = 1.2.3 + 2.3.4 + 3.4.5 + 4.5.6 +...+ 20.21.22
\(\Rightarrow4A=1.2.3.4+2.3.4.4+3.4.5.4+4.5.6.4+...+20.21.22.4\)
\(=1.2.3.4+2.3.4.\left(5-1\right)+3.4.5.\left(6-2\right)+4.5.6.\left(7-3\right)+...+20.21.22.\left(23-19\right)\)
= 1.2.3.4 + 2.3.4.5 -1.2.3.4 + 3.4.5.6 - 2.3.4.5 + 4.5.6.7 - 3.4.5.6 +...+ 20.21.22.23 - 19.20.21.22
= 20.21.22.23
= 212520
_Hok tốt_
!!!
\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{20.21.22}=\frac{1}{2}\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{20.21.22}\right)\)
\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+....+\frac{1}{20.21}-\frac{1}{21.22}\right)\)
\(=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{462}\right)=\frac{1}{2}.\frac{115}{231}=\frac{115}{462}\)
B=1.2.3+2.3.4+4.5.6+....+20.21.22
=>4B=4(1.2.3+2.3.4+3.4.5+...+20.21.22)
=>4B=1.2.3.4+2.3.4.4+3.4.5.4+...+20.21.22.4
=>4B=1.2.3.4+2.3.4.(5-1)+3.4.5.(6-2)+...+20.21.22(23-19)
=>4B=1.2.3.4+2.3.4.5-2.3.4+3.4.5.6-2.3.4.5+...+20.21.22.23-19.20.21.22
=>4B=20.21.22.23
=>4B=212520
=>B=53130
mình nha
Đặt A = 1 . 2 . 3 + 2 . 3 . 4 + 3 . 4 . 5 + 4 . 5 . 6 + ... + 20 . 21 . 22
=> 4A = 1 . 2 . 3 . 4 + 2 . 3 . 4 . 4 + 3 . 4 . 5 . 4+ 4 . 5 . 6 . 4 + ... + 20 . 21 . 22 . 4
=> 4A = 1 . 2 . 3 . ( 4 - 0 ) + 2 . 3 . 4 . ( 5 - 1 ) + 3 . 4 . 5 . ( 6 - 2 ) + 4 . 5 . 6 . ( 7 - 3 ) + ... + 20 . 21 . 22 . ( 23 - 19 )
=> 4A = 1 . 2 . 3 . 4 - 0 + 2 . 3 . 4 . 5 - 1 . 2 . 3 . 4 + 3 .4 . 5 . 6 - 2 . 3 . 4 . 5 + 4 . 5 . 6 . 7 - 3 . 4 . 5 . 6 + ... + 20 . 21.22.23 - 19.20.21.22
=> 4A = 0 + 20 . 21 . 22 . 23
=> 4A = 212520
=> A = \(\frac{212520}{4}=53130\)
* Công thức :
\(\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}\right)=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{6}\right)=\frac{1}{2}.\left(\frac{3}{6}-\frac{1}{6}\right)=\frac{1}{2}.\frac{2}{6}=\frac{1}{6}=\frac{1}{1.2.3}\)
\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{20.21.22}\)
\(=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{20.21}-\frac{1}{21.22}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{21.22}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{462}\right)\)
\(=\frac{1}{2}.\left(\frac{231}{462}-\frac{1}{462}\right)\)
\(=\frac{1}{2}.\frac{230}{462}\)
\(=\frac{115}{462}\)
Chúc bạn học tốt !!!
Câu 1:
Đặt S = 1.2+2.3+3.4+...+30.31
3 S = 1.2.3+2.3.3+3.4.3+...+30.31.3
3 S = 1.2.(3-0) + 2.3.(4-1) + 3.4.(5-2) + ...+ 30.31.(32-29)
3S = 1.2.3 + 2.3.4-2.3 + 3.4.5-2.3.4 + ...+ 30.31.32-29.30.31
3S= 30.31.32
S= 30.31.32/3
Vì sao mình phải nhân 2 vế cho 3 mà không phải là số khác vậy
a) Số hạng trong tổng có dạng n.(n+1)(n+2)
nhận xét: n(n+1)(n+2)(n+3) - (n-1).n(n+1)(n+2) = 4.n(n+1)(n+2). Tính A
4.A = 2.3.4.(5-1) + 3.4.5.(6-2) + ...+ 20.21.22.(23 - 19)
4.A = 2.3.4.5 - 1.2.3.4 + 3.4.5.6 - 2.3.4.5 + ...+ 20.21.22.23 - 19.20.21.22
4.A = (2.3.4.5 + 3.4.5.6 + ...+ 20.21.22.23) - (1.2.3.4 + 2.3.4.5 + ...+ 19.20.21.22)
4.A = 20.21.22.23 - 1.2.3.4 = 212 496 => A = 53 124
b) Em xem lại : dạng nào đã hỏi rồi , em nên tự làm