Tính A=1/2 x 2/3 x 3/4 x ...x 99/100
Tính A = 1/2*3/4*...*99/100
Cho A =1/2^2+1/3^2+1/4^2+.....+1/99^2+1/100^2
cho s=1/2^+1/3^2+...1/99^2+1/100^2 so sánh s với 1
Cho A=9/1×2+9/2×3+9/3×4+...+9/98×99+9/99×100
Tính:
a) \(A=1-2+2^2-2^3+...+2^{2002}\)
b) \(B=1-3+3^2-3^3+...+3^{98}-3^{99}\)
a, \(\left(1+\dfrac{1}{2}\right)\left(1+\dfrac{1}{2^2}\right)\left(1+\dfrac{1}{2^3}\right)\left(1+\dfrac{1}{2^4}\right)....\left(1+\dfrac{1}{2^{50}}\right)< 3\)
b, \(\dfrac{1}{2}-\dfrac{1}{2^2}+.........+\dfrac{1}{2^{99}}-\dfrac{1}{2^{100}}< \dfrac{1}{3}\)
1. Chứng minh:
\(\dfrac{1}{3}-\dfrac{2}{3^2}+\dfrac{3}{3^3}-\dfrac{4}{3^4}+...+\dfrac{99}{3^{99}}-\dfrac{100}{3^{100}}< \dfrac{3}{16}\)
2. Cho:
\(M=\dfrac{1}{15}+\dfrac{1}{105}+\dfrac{1}{315}+...+\dfrac{1}{1977}\). So sánh M với 12.
cho C=1+2+22+23+..............+299
chứng minh rằng C+1 là số có 31 chữ số
