It may take another 2016 years?

Consider a polynomial

\[\large f(x)=x^{2016}-x^{2015}+x^{2014}-x^{2013}\ldots-x^1+x^0\]

Then find

$\large f(2016)-f(2015)+f(2014)-f(2013)\ldots-f(1)+f(0)$

You can also post any other problems related to functions.

#Algebra

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Comments

here is the answer

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Aareyan Manzoor - 5 years, 5 months ago

Uhh... congratulations? Actually, how on earth did you get that?

Manuel Kahayon - 5 years, 5 months ago

wolframalpha

Aareyan Manzoor - 5 years, 5 months ago

The answer is indeterminate because $f(0) = 0^{2016} - 0^{2015} + \cdots + \color{#D61F06}{0^0}$ .

See What is $0^0$ .

Pi Han Goh - 5 years, 5 months ago

Then what will be the answer if we take out $f(0)$ , sir ?

Anish Harsha - 5 years, 5 months ago

The answer is very huge.

Hint: $\dfrac{x^n + 1}{x+1} = x^{n-1} - x^{n-2} + x^{n-2} - \cdots + 1$ for positive odd $n$ .

Pi Han Goh - 5 years, 5 months ago

2016

Aditya Rao - 5 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$