Question

If $A=2^{46},B=2^0+2^1+2^2+2^3+2^4+2^5+2^6+.........+2^{45}$, then which of the following is true?

• A. A < B
• B. A-B =2
• C. A>B
• D. Both B and C

Answer 1

The correct option is C

A>B

$A=2^{46}$

$B=2^0+2^1+2^2+2^3+2^4+2^5+2^6+.........+2^{45}$

$=\frac{(2^{46}-1)}{(2-1)}$

$=2^{46}-1$