Question: Use Laplace transforms to sum the following series or write as a single integral. a. (sum_{n=0}^{infty} frac{(-1)^{n}}{1+2 n}). b. (sum_{n=1}^{infty} frac{1}{n(n+3)}). c. (sum_{n=1}^{infty} frac{(-1)^{n}}{n(n+3)}). d.
Use Laplace transforms to sum the following series or write as a single integral.
a. \(\sum_{n=0}^{\infty} \frac{(-1)^{n}}{1+2 n}\).
b. \(\sum_{n=1}^{\infty} \frac{1}{n(n+3)}\).
c. \(\sum_{n=1}^{\infty} \frac{(-1)^{n}}{n(n+3)}\).
d. \(\sum_{n=0}^{\infty} \frac{(-1)^{n}}{n^{2}-a^{2}}\).
e. \(\sum_{n=0}^{\infty} \frac{1}{(2 n+1)^{2}-a^{2}}\).
f. \(\sum_{n=1}^{\infty} \frac{1}{n} e^{-a n}\).
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