Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
T/c:A=1/1*2*3+1/2*3*4+1/3*4*5+1/4*5*6+...+1/97*98*99+1/98*99*100
2A=2/1*2*3+2/2*3*4+2/3*4*5+2/4*5*6+...+2/97*98*99+1/98*99*100
2A=(1/1*2-1/2*3)+(1/2*3-1/3*4)+(1/3*4-1/4*5)+.....+(1/97*98-1/98*99)+(1/98*99-1/99*100)
2A=1/2+1/99*100
A=tự tính nha
Ta có: \(S=1\cdot2\cdot3+2\cdot3\cdot4+3\cdot4\cdot5+...+97\cdot98\cdot99\)
\(\Leftrightarrow4\cdot S=1\cdot2\cdot3\cdot\left(4-0\right)+2\cdot3\cdot4\cdot\left(5-1\right)+3\cdot4\cdot5\cdot\left(6-2\right)+...+97\cdot98\cdot99\cdot\left(101-97\right)\)
\(\Leftrightarrow4\cdot S=98\cdot99\cdot100\cdot101\)
\(\Leftrightarrow S=\text{24497550}\)
Đặt S = 1/1.2.3 - 1/2.3.4 - 1/3.4.5 - ...- 1/97.98.99
S x 2 = 2/1.2.3 - 2/2.3.4 - 2/3.4.5 - ...- 2/97.98.99
= (1/1.2 -1/2.3) - (1/2.3 - 1/3.4 ) - (1/3.4 - 1/4.5) - ...- (1/97.98 - 1/98.99)
= 1/1.2 - 1/2.3 - 1/2.3 + 1/3.4 - 1/3.4 + 1/4.5 - ....- 1/97.98 + 1/98.99
= 1/2 -1/3 + 1/98.99
= 1618/9072 => S = 1618/9072 : 2 = 809/9072
4E=1.2.3.4+2.3.4.(5-1) + 3.4.5.(6-2)+....+96.97.98.(99-95) + 97.98.99.(100-96)
4E = 1.2.3.4 + 2.3.4.5 - 1.2.3.4 + 3.4.5.6 - 2.3.4.5 +....+ 96.97.98.99 - 95.96.97.98 + 97.98.99.100 - 96.97.98.99
(Để ý những số này sẽ được lược bỏ)
4E= 97.98.99.100
=>E = 97.98.99.25 = 23527350
A= 1.2.3 + 2.3.4 + 3.4.5 +.....+ 98.99.100
4A = 98.99.100.4 + .....+ 3.4.5.4 + 2.3.4.4 + 1.2.3.4
4A = 98.99.100.(101-97) +... + 2.3.4.(5-1) + 1.2.3.4
4A = 98.99.100.101 - 97.98.99.100+......+2.3.4.5 - 1.2.3.4 + 1.2.3.4
4A = 98.99.100.101
A = 98.99.100.101 : 4
A = 24497550
Đặt B, ta có:
\(2B=\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{98.99.100}\)
\(=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{98.99}-\frac{1}{99.100}\)
Thấy:
\(-\frac{1}{2.3}+\frac{1}{2.3}=0;-\frac{1}{3.4}+\frac{1}{3.4}=0\)
\(\Rightarrow2B=\frac{1}{2}-\frac{1}{99.100}=\frac{1}{2}-\frac{1}{9900}=\frac{4950}{9900}-\frac{1}{9900}=\frac{4949}{9900}\)
\(\Rightarrow B=\frac{4949}{9900}:2=\frac{4949}{19800}\)
\(B=1\cdot2\cdot3+2\cdot3\cdot4+3\cdot4\cdot5+...+98\cdot99\cdot100\)
\(\Rightarrow4B=4\cdot\left(1\cdot2\cdot3+2\cdot3\cdot4+...+98\cdot99\cdot100\right)\)
\(\Rightarrow4B=1\cdot2\cdot3\cdot\left(4-0\right)+2\cdot3\cdot4\cdot\left(5-1\right)+3\cdot4\cdot5\cdot\left(6-2\right)+...+98\cdot99\cdot100\cdot\left(101-97\right)\)
\(\Rightarrow4B=1\cdot2\cdot3\cdot4+2\cdot3\cdot4\cdot5-1\cdot2\cdot3\cdot4-....+98\cdot99\cdot100\cdot101-97\cdot98\cdot99\cdot100\)
\(\Rightarrow4B=98\cdot99\cdot100\cdot101\)
\(\Rightarrow B=\dfrac{98\cdot99\cdot100\cdot101}{4}\)
\(\Rightarrow B=25\cdot98\cdot99\cdot101\)
B=1x2x3+2x3x4+...+98x99x100
=>4B=1x2x3x(4-0)+2x3x4x(5-1)+...+98x99x100x(101-97)
4B=1x2x3x4+2x3x4x5-1x2x3x4+...+98x99x100x101-97x98x99x100
4B=98x99x100x101
=>B=\(\dfrac{98\cdot99\cdot100\cdot101}{4}\)=24497550.