First slide

Geometric progression

Question

$If (1 + x) (1 + x^{2}) (1 + x^{4}) \dots (1 + x^{128}) = \sum_{r = 0}^{n} x^{r} then n is$

Moderate

A

255
B

127
C

60
D

256

Solution

${(1+x)(1+x}^{2} {)(1+x}^{4}) ... {(1+x}^{128})=1+x+ ... {+x}^{n} = \frac{{1-x}^{n+1}}{1-x} (s u m o f n' t e r m s i n G . P = \frac{a (1 - r^{n})}{1 - r})$
$\begin{array}{l} \to 1 - x^{256} = 1 - x^{n + 1} \\ \to n + 1 = 256 = n = 255 \end{array}$

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