Question

a ) So sánh các lũy thữa sau 2¹⁰⁰ và  1024 ⁹

b) Cho S = 2 + 2² + 2³ + .........+ 2¹⁰⁰ 

Chứng minh S chia hết cho 5

Answer 1

a) \(1024^9=\left(2^{10}\right)^9=2^{10.9}=2^{90}\)

MÀ \(2^{90}<2^{100}\Rightarrow2^{100}>1024^9\)

b) \(S=2+2^2+2^3+....+2^{100}\)

\(S=\left(2+2^2+2^3+2^4\right)+.....+\left(2^{97}+2^{98}+2^{99}+2^{100}\right)\)

\(S=2.15+2^5.15+.....+2^{97}.15\)

\(S=5.3.\left(2+2^5+....+2^{100}\right)\)

Vậy S chia hết cho 5