- #1
AdityaDev
- 527
- 33
Homework Statement
If ##|P(x)|<=|e^{x-1}-1|## for all x> 0 where ##P(x)=\sum\limits_{r=0}^na_rx^r## then prove that ##|\sum\limits_{r=0}^nra_r|<=1##
Homework Equations
None
The Attempt at a Solution
##P(1)=a_0+a_1+...##
If the constants are positive, then ##P(1)<=|e^0-1|##
So P(1)<=0
so ##a_0+a_1+a_2+... <=1##
But how do I prove that ##0a_0+1.a_1+2.a_2+...<=1##