If $x = 2$ , then $x^{9} + x^{8} + x^{7} + . . . . . . . . . . . . . . + x^{1} + 1$ =

1032

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1203

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1023

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2032

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Solution

The correct option is C $1023$
Given,

$x = 2$

$x^{9} + x^{8} + x^{7} + . . . . . . . . . + 1$

$= 1 + x + x^{2} + . . . . . . . . . . . + x^{9}$

$= 1 + 2 + 2^{2} + 2^{3} + 2^{4} + 2^{5} + 2^{6} + 2^{7} + 2^{8} + 2^{9}$

$= 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512$

$= 1023$

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