\(E=1.1+2.2+3.3+4.4+...+99.99\)
\(\Rightarrow E=1^2+2^2+3^2+4^2+...+99^2\)
\(\Rightarrow E=\dfrac{99.\left(99+1\right)\left(2.99+1\right)}{6}\)
\(\Rightarrow E=\dfrac{99.100.199}{6}\)
\(\Rightarrow E=33.50.199=328350\)
E = 1 x 1 + 2 x 2 + 3 x 3 + 4 x 4 +...+ 99 x 99
E = 1x(2-1) + 2 x (3-1)+...+ 99 x (100 -1)
D = 1 x 2 - 1 + 2 x 3 - 2 +...+ 99 x 100 - 99
D = 1x2 + 2 x 3 +...+ 99 x 100 - ( 1 + 2 +...+ 99)
Đặt A = 1x2 + 2 x 3 +...+ 99 x 100
B = 1 + 2 + ...+ 99
1x2 x 3 = 1x2x3
2x3x3 = 2x 3 x (4-1) = 2x3x4 - 1x2x3
3 x 4 x 3 = 3 x 4 x ( 5 - 2) = 3 x 4 x 5 - 2 x 3 x 4
................................................
99 x 100 x 3 = 99 x 100 x (101 - 98) = 99x100x101 - 98 x 99 x 100
Cộng vế với vế ta có: 3A = 99 x 100 x 101
A = 99 x 100 x 101 : 3 = 333300
B = 1 + 2 + 3 + ...+ 99
B = (99 + 1).[(99 -1):1 +1]:2 = 4950
E = 33300 - 4950 = 328350
a là cocaiconcac nhé e
b là cocaidaccau ok nhé
Bạn kaito kid không được nói tục nhé
\(...\Rightarrow G=1.100+2.\left(100-1\right)+3.\left(100-2\right)+...+99.\left(100-98\right)+100.\left(100-99\right)\)
\(\Rightarrow G=100.\left(1+2+3+...+100\right)-\left(1.2+2.3+3.4+...+98.99+99.100\right)\)
\(\Rightarrow G=100.\dfrac{100.101}{2}-\dfrac{100.101.102}{3}\)
\(\Rightarrow G=50.100.101-100.101.34\)
\(\Rightarrow G=100.101.\left(50-34\right)\)
\(\Rightarrow G=100.101.16=161600\)
G = 1 x 100 + 2 x 99 + 3 x 98+...+ 99 x 2 + 100 x 1
G = 1 x (101 - 1) + 2 x ( 101 - 2) +...+ 100 x ( 101 - 100)
G = 1 x 101 - 1 x 1 + 2 x 101 - 2 x 2 +...+ 100 x 101 - 100 x 100
D = (1 x 101 + 2 x 101 +...+ 100 x 101) - ( 1x1 + 2 x 2 +...+ 100x 100)
D = 101 x ( 1 + 2 + ...+ 100) - (1 x1 + 2 x 2 +...+ 100 x 100)
Đặt A = 101 x( 1 + 2 +...+ 100)
B = 1 x 1 + 2 x 2 +...+ 99 x 99 + 100 x 100
A = 101 x [ (100 + 1) x 100:2] = 510050
B = 328350 + 100 x 100 = 338350
G = A - B = 510050 - 338350 = 171700
