If a satisfies the equation a 2017 − 2 a + 1 = 0 and S = 1 + a + a 2 + ⋯ + a 2016 , then the possible value(s) of S is/are

If a = 1 , then S = 2017 . If a  = 1 , then S = a − 1 a 2017 − 1 , and since a 2017 = 2 a − 1 , S = a − 1 2 ( a − 1 ) = 2 .

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Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesG.P.Medium2 minQB

MathematicsMediummultiple choice

If $a$ satisfies the equation $a^{2017} - 2 a + 1 = 0$ and $S = 1 + a + a^{2} + \dots + a^{2016}$ , then the possible value(s) of $S$ is/are

Options:(select one or more)

Answer:

C, D

Solution:

If $a = 1$ , then $S = 2017$ . If $a \neq = 1$ , then $S = \frac{a ^{2017} - 1}{a - 1}$ , and since $a^{2017} = 2 a - 1, S = \frac{2 ( a - 1 )}{a - 1} = 2$ .

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:G.P.

⏱ 2mℹ️ Source: QB

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