Question

So sánh B = 2 mũ 1 + 2 mũ 3 + 2 mũ 5 + chấm chấm chấm + 2 mũ 99 và F = 2 mũ 101 - 2

Answer 1

2B= 2²+2³+2⁴+...+2¹⁰⁰

=>B=2B-B=2²+2³+2⁴+...+2¹⁰⁰-(2¹+2²+2³+...+2⁹⁹)=2¹⁰⁰-2<2¹⁰¹-1

Answer 2

\(B=2^1+2^3+2^5+...+2^{99}\)

\(2^2B=2^2\left(2+2^3+2^5+...+2^{99}\right)\)

\(4B=2^3+2^5+2^7+...+2^{101}\)

\(4B-B=\left(2^3+2^5+2^7+...+2^{101}\right)-\left(2^1+2^3+2^5+..+2^{99}\right)\)

\(3B=2^{101}-2\)

\(B=\frac{2^{101}-2}{3}\) < \(F=2^{101}-2\)

Answer 3

thanks