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Question Number 41721 by Rio Michael last updated on 11/Aug/18
showthatUn=1+nx+n(n−1)2!x2+n(n−1)(n−2)3!x3+....forwhichUn=(1+x)n.
Commented by maxmathsup by imad last updated on 12/Aug/18
letp(x)=(1+x)nwehavep(x)=∑k=0∞p(k)(0)k!xk=∑k=0np(k)(0)k!xk+∑k=n+1∞p(k)(0)k!butfork>np(k)(x)=0⇒p(x)=∑k=0np(k)(0)k!xkbutbinomialformulaegivep(x)=∑k=0nCnkxk=Cn0+Cn1x+Cnnx2+....+Cnnxn=1+nx+n(n−1)2x2+.....+xn(sothesumisnotinfinite)
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