frozen prairie
I have this question here which I tried to do but I could not work out how to do part iii. After a while I tried look at the mark scheme as well but I still couldn't quite understand it. Why is it significant that k>i? Why must that be true for ai to be constant
ashen inletBOT
hearty wasp
I have this question here which I tried to do but I could not work out how to do...
$(1+x^k)P(x)=P(x)+x^kP(x)$
If you want to only look for the coefficient of $x^i$ where $i<k$, then that coefficient can be found in the $P(x)$ part of the sum
modest acornBOT
Element118
frozen prairie
$(1+x^k)P(x)=P(x)+x^kP(x)$
If you want to only look for the coefficient of $x^i$...
why does this prove that a is constant for every degree of x in p(x)?
hearty wasp
Essentially what you want to prove is that the coefficient of $x^i$ would eventually be as in $p_i(x)$
modest acornBOT
Element118
hearty wasp
$p_{i+1}(x)=(1+x^{i+1})p_i(x)=p_i(x)+x^{i+1}p_i(x)$
modest acornBOT
Element118
hearty wasp
and only the $p_i(x)$ part matters here
modest acornBOT
Element118
frozen prairie
and only the $p_i(x)$ part matters here
ive been taking a while to think about it but im still not quite sure i understand
hearty wasp
ive been taking a while to think about it but im still not quite sure i understa...
consider the coefficient of $x^i$ on both sides