Question

H = 1 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + ... + 2^2009

k = 2^2010 - 1

So sanh k va H

 

Answer 1

\(H=1+2+2^2+2^3+2^4+....+2^{2009}\)

\(\Rightarrow2H-H=\left(2+2^2+2^3....+2^{2010}\right)-\left(1+2+2^2+...+2^{2009}\right)\)

\(\Rightarrow H=2^{2010}-1=K\)

Answer 2

2.H = 2 + 2² + 2³ + ... + 2²⁰¹⁰

2.H - H = (2 + 2² + 2³ + ... + 2²⁰¹⁰) - (1 + 2 + 2² + ... + 2²⁰⁰⁹)

H = 2²⁰¹⁰ - 1 = k