Fun with implicit function and infinite sum

Algebra Level 3

{ f : R → R f ( 0 ) = 1 f ( x y + 1 ) = f ( x ) f ( y ) − f ( y ) − x + 2 \begin{cases} f:\mathbb{R}\rightarrow{}\mathbb{R} \\ f(0)=1 \\ f(xy+1)=f(x)f(y)-f(y)-x+2 \end{cases}

Evaluate

∑ i = 1 ∞ 1 2 f ( i − 2 ) \sum_{i=1}^{\infty}{\frac{1}{2^{f(i-2)}}}


The answer is 2.

Bernardo Sulzbach by Bernardo Sulzbach , 30, Brazil

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

3 solutions

My solution

Image Image

2 Helpful 0 Interesting 1 Brilliant 0 Confused
Ramiel To-ong
Jun 5, 2015

Using sum to infinity..where r = 0.5 S =2

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Fox To-ong
Dec 21, 2014

Using sum to infinity..where r = 0.5 S =2

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...