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I need to graph the following function

$f(t) = 1 + \sum_{n=1}^\infty(-1)^n u(t-n)$

($u$ refers to the unit step function)

and find the laplace transform of this function.

The problem is similar to another one posted here Calculate the Laplace transform except for mine i need to graph a function and it is slightly different.

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    If $t>0$, $u(t-0) = 1$, so the Laplace transforms will be the same. Why don't you just graph the functions $t \mapsto 1-u(t-1)$, and $t \mapsto 1-u(t-1)+u(t-2)$ and guess what the general pattern is. The graph is fairly simple.2012-05-19
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    me and a classmate sketched the graph,2012-05-19
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    me and a classmate sketched a graph that looked like f(1) = 1 + (-1) = 0 f(2) = 1 + (-1) +1 = 1 f(3) = 1 + (-1) +1 + (-1) = 0 f(4) = 1 + (-1) +1 + (-1) +1 = 1 not to sure if that's how you sketch piecewise functions2012-05-19
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    It should look like a square wave...2012-05-19
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    so from 0 to 1 f(t) = 0 and from 1 to 2 f(t) = 1 (from here it repeated itself) and we took the laplace 1/(1-e^(-sT) * integral from 0 to 2 of e^-(st)f(t)dt which is than split up into two integrals, the first from 0 to 1 (but since f(t) is 0 on this range it becomes 0) the second from 1 to 2 1/(1-e^(-2s) integral from 1 to 2 e^-(st)dt and i'm not sure if we simplified it right, but the answer came out to 1/(s(e^s+1)2012-05-19
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    Yeah i looked up pictures of the square wave on google,2012-05-19
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    my graph didn't look like it :(2012-05-19

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