For x   ∈ R ,   x ≠ - 1 , if 1 + x 2016 + x 1 + x 2015 + x 2 1 + x 2014 + … + x 2016 = ∑ i = 0 2016 a i x i , then a 17 is equal to

Question

For x &#160; &#8712; R , &#160; x &#8800; - 1 , if 1 + x 2016 + x 1 + x 2015 + x 2 1 + x 2014 + &#8230; + x 2016 = &#8721; i = 0 2016 a i x i , then a 17 is equal to

Aicharya · Accepted Answer

S = 1 + x 2016 + x 1 + x 2015 + x 2 1 + x 2014 + &#8230; &#8230; + x 2015 1 + x + x 2016 &#160; &#160; . . . i x 1 + x &#160; S = x &#160; 1 + x 2015 + x 2 1 + x 2014 + &#8230; + x 2016 + x 2017 1 + x &#160; &#160; . . . i i i i - i S 1 + x = 1 + x 2016 - x 2017 1 + x &#8756; S = 1 + x 2017 - x 2017 Coefficient a 17 = 2017 C 17 &#160; = 2017 ! 17 ! 2000 !

For x   ∈ R ,   x ≠ - 1 , if 1 + x 2016 + x 1 + x 2015 + x 2 1 + x 2014 + … + x…

Solution

For x &#160; &#8712; R , &#160; x &#8800; - 1 , if 1 + x 2016 + x 1 + x 2015 + x 2 1 + x 2014 + &#8230; + x…

Solution

For x ∈ R , x ≠ - 1 , if 1 + x 2016 + x 1 + x 2015 + x 2 1 + x 2014 + … + x…