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Khỏi cần tích.
A=1.22+2.32+...+2017.20182
=(2-1).22+(3-1).32+...+(2018-1).20182
=23+33+43+...+20183 - (22+32+...+20182)
=(13+23+...+20183)-(12+22+...+20182)
Ta có: 4k3=(k4+2k3+k2)-(k4-2k3+k2)=[(k+1)k]2-[k(k-1)]2
=>
4.20183=(2019.2018)2-(2018.2017)2
4.20173=(2018.2017)2-(2017.2016)2
...
4.23=(3.2)2-(2.1)2
4.13=(2.1)2-(1.0)2
Cộng 2 vế:
4(13+23+...+20183)=(2019.2018)2 => 13+23+...+20183=(2019.2018)2 /4
Lại có:
6.k2=[2(k+1)3-3(k+1)2+(k+1)] - [2.k3-3k2+k]
=>
6.20182=(2.20193-3.20192+2019)-(2.20183-3.20182+2018)
6.20172=(2.20183-3.20182+2018)-(2.20173-3.20172+2017)
....
6.22=(2.33-3.32+3)-(2.23-3.22+2)
6.12=(2.23-3.22+2)-(2.13-3.12+1)
Cộng 2 vế:
6(12+22+...+20182)=(2.20193-3.20192+2019) =>12+22+...+20182=(2.20193-3.20192+2019)/6
=>
A=[(2019.2018)2 /4] - [(2.20193-3.20192+2019)/6]
A = 1.22 + 2.32 + 3.42 + …. + 99.1002
A= 1.2.2 + 2.3.3 + 3.4.4 +...+99.100.100
A= 1.2(3-1) +2.3(4-1) +3.4(5-1) +....+ 99.100(101-1)
A= 1.2.3 - 1.1.2 + 2.3.4 - 1.2.3 + 3.4.5 - 1.3.4 +...+99.100.101- 1.99.100
A= 1.2.3 + 2.3.4 + 3.4.5+....+99.100.101 - 1.2 +2.3 + 3.4+...+ 99.100
A= 24497550 - 333300
A=24164250
Vậy...
* Khai triển
1.2^2 = 1.2.2 = 1.2.(3 - 1) = 1.2.3 - 1.2
2.3^2 = 2.3.3 = 2.3.(4 - 1) = 2.3.4 - 2.3
3.4^2 = 3.4.4 = 3.4(5 - 1) = 3.4.5 - 3.4
.....................................................
98.99^2 = 98.99.99 = 98.99.100 - 98.99
Vậy
E = 1.2.3+2.3.4 + 3.4.5 + ... + 98.99.100 - (1.2 + 2.3 + 3.4 + ..+ 98.99) = X - Y
Ta có
X = 1.2.3+2.3.4 + 3.4.5 + ... + 98.99.100
X.4 = 1.2.3.4 + 2.3.4.(5 - 1) + 3.4.5.(6 - 2) +....+98.99.100.(101-97) = 98.99.100.101
=> X = 98.99.100.101/4 = ....
Y = 1.2 + 2.3 + 3.4 + ..+ 98.99
Y.3 = 1.2.3 + 2.3.(4-1) + 3.4.(5-2) + .. + 98.99.(100-97) = 98.99.100
=> Y = 98.99.100/3 = ...
Vậy E = X - Y = .... - .... = 24174150
hahahahaha
xet A va B thi ta thay B la cac so binh phuong cong vao con A thi lai la cac so nhan nhau lien tiep neu de y ta thay neu lay 1*2-1=1....va tru thanh day so lien den 98
A-B=1+2+3+........................+98 co 98 so hang
A-B=(1+98)*98:2=4851
A=1.22+2.32+..............+(n-1).n2
A=1.2.2+2.3.3+.......+(n-1).n.n
A=1.2.(3-1)+2.3.(4-1)+.........+(n-1).n.(n+1-1)
A=1.2.3-1.2+2.3.4-2.3+..........+(n-1).n.(n+1)-(n-1).n
A=[1.2.3+2.3.4+.........+(n-1).n.(n+1)]-[1.2+2.3+............+(n-1).n)
Bạn tự làm tiếp nhá
