Find the first three nonzero terms of the taylor series for e^x + e^(-x)...

I know the expansion of both terms but im not sure how to add them to find the expansion!

Question

Find the first three nonzero terms of the taylor series for e^x + e^(-x)...

I know the expansion of both terms but im not sure how to add them to find the expansion!

megannicole51 · Answer

@ganeshie8

ganeshie8 · Answer

put the both expansions first

ganeshie8 · Answer

btw, you expanding it about 0 right ?

megannicole51 · Answer

e^x=1+x+x^2/2!+x^3/3!+....
e^(-x)=1-x+x^2/2!-x^3/3!+....

ganeshie8 · Answer

yes, clearly all odd powers cancel out.. .
so simply add the remaining even powers

ganeshie8 · Answer

e^x          =   1+x+x^2/2!+x^3/3!+.... 
e^(-x)       =   1-x+x^2/2!-x^3/3!+....
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e^x + e^(-x) = 2 + 2*x^2/2! + 2*x^4/4! + .....

megannicole51 · Answer

oh okay that makes sense!:) thank you!

ganeshie8 · Answer

np :)