find the remainder when 1+x+x^2.....+x^2017 is divided with 1+x
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(1+x+x^2.....+x^2017 ) ÷ (1+x)
x= -1 [1+ x = 0]
Substitute the value of x
1 + -1 +(-1)^2 +(-1)^3+(-1)^4...... (-1)^2015 +(-1)^2016 +(-1)^2017
= 1 + -1 + 1 + -1 ....... -1 + 1 -1
= 0
So by remainder theorem the remainder will be 0 when (1+x+x^2.....+x^2017 ) is divided by( x+1)
x= -1 [1+ x = 0]
Substitute the value of x
1 + -1 +(-1)^2 +(-1)^3+(-1)^4...... (-1)^2015 +(-1)^2016 +(-1)^2017
= 1 + -1 + 1 + -1 ....... -1 + 1 -1
= 0
So by remainder theorem the remainder will be 0 when (1+x+x^2.....+x^2017 ) is divided by( x+1)
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