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## 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##