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The co-efficient of x^(401) in the expansion of (1+x+x^(2)+......+x^(9))^(-1),(|x|

 The co-efficient of x^(401) in the expansion of (1+x+x^(2)+......+x^(9))^(-1),(|x|

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Grade:12th pass

1 Answers

Arun
25750 Points
4 years ago
Dear Sahil
 
it can be written as ((x^10 – 1) / (x – 1) ) –1
 
(x – 1) (x^10 – 1)^-1 = (-1)^-1 (x – 1) (1 –  x^10)^-1
 
for coefficient of x^409
(-1)^-1 (1 +408 – 1)C408 –   (-1)^-1 (1+ 409 -1)C409 
 
= (-1)^-1 – (-1)^-1 = 0

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