How do you use a power series to find the exact value of the sum of the series #1+sqrt(2)+2/(2!) +(sqrt(2))^3/(3!) +4/(4!) + …# ? Calculus Power Series Power Series and Exact Values of Numerical Series 1 Answer Wataru Sep 19, 2014 Since #1+x+x^2/{2!}+x^3/{3!}+x^4/{4!}+cdots=e^x#, #1+sqrt{2}+{(sqrt{2})^2}/{2!}+{(sqrt{2})^3}/{3!}+{(sqrt{2})^4}/{4!}+cdots=e^{sqrt{2}}# Answer link Related questions How do you use a power series to find the exact value of the sum of the series #1+2+4/(2!)... How do you use a power series to find the exact value of the sum of the series #1-1/2+1/3-1/4 + …# ? How do you use a power series to find the exact value of the sum of the series... How do you use a power series to find the exact value of the sum of the series... How do you use a power series to find the exact value of the sum of the series #1+e+e^2 +e^3 +e^4 + …# ? How do you use a power series to find the exact value of the sum of the series... How do you use a power series to find the exact value of the sum of the series... See all questions in Power Series and Exact Values of Numerical Series Impact of this question 1834 views around the world You can reuse this answer Creative Commons License