\(B=3^{100}-2^{100}+3^{98}-2^{98}\)
\(B=\left(3^{100}+3^{98}\right)-\left(2^{100}+2^{98}\right)\)
\(B=3^{98}\left(3^2+1\right)-2^{98}\left(2^2+1\right)\)
\(B=3^{98}.10-2^{98}.5\)
\(B=3^{98}.10-2^{97}.10\)
\(B=10\left(3^{98}-2^{97}\right)\)
Vì \(10\left(3^{98}-2^{97}\right)⋮10\)
\(\Rightarrow B⋮10\)
B=3100-399+398-397+....+32-3+1
|-100-98-...-1+1+2+3+...+99| =
a) 1+3-5-7+9+11-....-397-399
b) 1+2-3-4+5+6-....-99-100
c) 2-5+8-11+14-17+....+98-101
1 x 2 x 3 + 2 x 3 x 4 + ..... + 98 x 99 x 100
a) 1+3-5-7+9+11-......-397-399
b) 1+2-3-4+5+6-....-99+100
c) 2-5+8-11+14-17+....+98-101
Tính tổng các dãy số sau
a.100-99+98-97+96-95+...+4-3+2-1
b.200-199+198-197+...+4-3+2-1
Tính: \(A=2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-3\)
Tính giá trị biểu thức A , biết rằng A = M : N
Mà M = \(\dfrac{\dfrac{1}{99}+\dfrac{2}{98}+\dfrac{3}{97}+\dfrac{4}{96}+...+\dfrac{97}{3}+\dfrac{98}{2}+\dfrac{99}{1}}{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}+...+\dfrac{1}{100}}\)
N = \(\dfrac{92-\dfrac{1}{9}-\dfrac{2}{10}-\dfrac{3}{11}-...-\dfrac{90}{98}-\dfrac{91}{99}-\dfrac{92}{100}}{\dfrac{1}{45}+\dfrac{1}{50}+\dfrac{1}{55}+...+\dfrac{1}{495}+\dfrac{1}{500}}\)
Rút gọn :
A = \(3^{100}-3^{99}+3^{98}-3^{97}+......+3^2-3+1\)
