Find the remainder when 1+x+x2+x3+. . . +x2018 is . . .

Question : Find the remainder when 1+x+x²+x³+. . . +x²⁰¹⁸ is divided by (x-1).

Doubt by Gauri

Solution: 

p(x) = 1+x+x²+x³+. . .+x²⁰¹⁸

g(x) = x-1

By Remainder Theorem 

g(x) = 0
x-1=0
x=1
Remainder = p(1)

p(1) = 1+(1)+(1)²+(1)³+. . .+(1)²⁰¹⁸

p(1) = 1 + (1×2018)
p(1) = 1 + 2018
p(1) = 2019

Hence, the required remainder is 2019

Similar Question : 

⭐ Find the remainder when 1+x+x²+x³+. . . +x²⁰¹⁸ is divided by (x+1).
Ans : 1