Geometric Sum
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Part a. Determine a closed-form expression for the following sum:
S_N=\sum_{n=0}^{N-1}a^n
Hint: Compare S_N to aS_N.
Is your closed-form expression valid for all a and N? If not, determine alternative expressions for these (and any other) edge cases.
Part b. Determine a closed-form expression for the following sum:
S_\infty=\sum_{n=0}^\infty a^n
Is your closed-form expression valid for all a?
Explain.
Part c. Determine a closed-form expression for the following sum (with infinitely many terms):
S_d=1+2a+3a^2+4a^3+5a^4+\cdots
Hint: Differentiate.
Is your closed-form expression valid for all a? Explain.
Upload your solution to this problem (including parts a, b, and c) as a single pdf file.
Your most recent submission before the problem deadline is the one that will be graded.
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Your most recent submission before the problem deadline is the one that will be graded.
