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Question Number 170198 by Mastermind last updated on 18/May/22
Find the first three term of the series  for e^x ln(1+x)    Mastermind
Findthefirstthreetermoftheseriesforexln(1+x)Mastermind
Answered by Mathspace last updated on 18/May/22
e^x =Σ_(n=0) ^∞ (x^n /(n!))=1+x +(x^2 /2) +(x^3 /6)+o(x^4 )  ln^((1)) (1+x)=(1/(1+x))=1−x+x^2 −x^3 +o(x^4 ) ⇒  e^x ln(1+x)=(1+x+(x^2 /2)+(x^3 /6)+o(x^4 ))(1−x+x^2 −x^3 +o(x^4 ))  =1−x+x^2 −x^3 +x−x^2 +x^3 −x^4   +(x^2 /2)−(x^3 /2)+(x^4 /2)−(x^5 /2)+(x^3 /6)−(x^4 /6)+(x^5 /6)−(x^6 /6)+o(x^6 )  =....
ex=n=0xnn!=1+x+x22+x36+o(x4)ln(1)(1+x)=11+x=1x+x2x3+o(x4)exln(1+x)=(1+x+x22+x36+o(x4))(1x+x2x3+o(x4))=1x+x2x3+xx2+x3x4+x22x32+x42x52+x36x46+x56x66+o(x6)=.
Commented by Mastermind last updated on 20/May/22
That′s last answer?
Thatslastanswer?
Commented by Mastermind last updated on 19/May/22
thanks sir
thankssir

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