- 2017
- 2019
- 2020
- 2018

Option 4 : 2018

**Given:**

The expression 1 + x + x^{2} + …………… + x^{2017 }is divided by x - a

**Calculation**

The remainder theorem states that when a polynomial f(x) and linear polynomial x – a the

The remainder of the division will be f(a)

f(a) = 1 + x + x ^{2 } + ………. X^{2017}

Linear polynomial x -1

Therefore, remainder when 1 + x + x^{2 }+ x^{2017}

it is divided by (x - 1) is f(a) = 1 + 1 + 1^{2} + … 1^{2017 } = 2018

Hence, remainder = 2018

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