Question

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Answer 1

Rewrite as \[5x*(1/(1-(-1/2)*x))\]

Remember that the power series for 1/(1=anything) is 1+anything+anything^2+...
Here, our anything is -1/2, leading us to the power series \[1-x/2+x^2/4-x^3/8+x^4/16-x^5/32+...\]

So we can write that power series as \[\sum_{x=0}^{\infty}(-1/2)^{n}x ^{n}\]

Multiply by 5x to get \[\sum_{x=0}^{\infty}5*(-1/2)^{n}x ^{n+1}\]. Use that and n=0,1,2,3,4,5 to finish up the WebWoRks