Next Step Polynomial

Algebra Level 3

If f ( x ) f(x) is a polynomial of odd degree n n such that f ( 0 ) = 0 , f ( 1 ) = 1 2 , … , f ( n ) = n n + 1 f(0)=0,f(1)=\dfrac{1}{2},\ldots,f(n)=\dfrac{n}{n+1} , then find f ( n + 1 ) . f(n+1).


The answer is 1.

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Atul Shivam by Atul Shivam , 23, India

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2 solutions

Barr Shiv
Nov 30, 2018

f(x)=0.5x easy

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Ron Nissim
Jun 11, 2018

See USAMO 1975 Problem 3 https://artofproblemsolving.com/wiki/index.php?title=1975 USAMO Problems/Problem_3

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