If \(f(x)\) is a polynomial satisfying relation \(f(x)=\dfrac{k}{k+1}\) for \({k=1,2,3,\ldots,100}\) except \(k=a\) where \(a\) is a natural numbers and belongs to \((0,100)\) and \(f(101)=1\).Find \(\dfrac{1-f(a)}{f'(a)}\) .

There are multiple polynomials that satisfy the conditions since we can add \( A (x-1)(x-2)\ldots (x-101) \). This suggests that you want the degree to be 100.

The condition should be \( f(k) = \frac{k}{k+1} \) instead?

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestTry reading the first section of polynomial interpolation - remainder factor theorem.

Addendum: Oh wait... this problem is not as easy as it looks. Give me one moment to think about this...

Log in to reply

Several issues with your problem

Log in to reply