Applied Course | Mock GATE | Test 1 | Question: 40

Question

$\begin{array}{l} A = 2000 \\ B = A - 999 \\ C = A + B - 998 \\ D = A + B + C - 997 \\ \vdots \\ \vdots \\ Z = A + B + C + \dots + Y - 975 \end{array}$
How much $\frac{Z+1}{2^{25}}$? ____

Answer 1

The value of $B = 1001$
And we can see that $C = 2B + 1 \Rightarrow  2B + (2-1)$
$D=2C+1=4B+3 \Rightarrow 2^2B+(2^2-1)$
$E =2D+1=8B+7 \Rightarrow 2^3B+(2^3-1)$
$\vdots$
$\vdots$
$Z=2Y+1 \Rightarrow 2^{24}B+(2^{24}-1)$
Now $\frac{Z+1}{2^{25}} = \frac{2^{24}(B+1)-1]+1)}{2^{25}} = \frac{B+1}{2}=501$