Question

A= 1 + 2 + 4 + 8 + 16 + 32 +...... + 2^2003

​

Answer 1

 

$\displaystyle\bf\\A= 1 + 2 + 4 + 8 + 16 + 32 +...+ 2^{2003}\\\\A=2^0+2^1+2^2+2^3+2^4+2^5+...+2^{2003}\\\\A=\frac{2^{2003+1}-1}{2-1}\\\\A=\frac{2^{2004}-1}{1}\\\\\boxed{\bf A=2^{2004}-1}$