For the following problems, draw the given function and find the Laplace transform in closed form. a.

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For the following problems, draw the given function and find the Laplace transform in closed form.

a. \(f(t)=1+\sum_{n=1}^{\infty}(-1)^{n} H(t-n)\).

b. \(f(t)=\sum_{n=0}^{\infty}[H(t-2 n+1)-H(t-2 n)]\).

c. \(f(t)=\sum_{n=0}^{\infty}(t-2 n)[H(t-2 n)-H(t-2 n-1)]+(2 n+2-t)[H(t-\) \(2 n-1)-H(t-2 n-2)]\).

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