Question

Let $a\in (0,1]$ satisfies the equation $a^{2008}-2a+1=0$ and $S=1+a+a^2+.....+a^{2007}$. Sum of all possible value(s) of $S$, is

• A. $2010$
• B. $2009$
• C. $2008$
• D. $2$

Answer 1

The correct option is A $2010$

Given, $a\in (0,1]$

$a^{2008}-2a+1=0$

$a^{2008}-1=2(a-1)$

$\frac{a^{2008}-1}{a-1}=2$ ....... (1)

$S=1+a+a^2+a^3+....+a^{2007}$

GP Sum

$S=\left(1\right)\frac{(a^{2008}-1)}{a-1}$

From (1)

$⟹S=2$