Question

Use the geometric series f(x) = 1 / (1 - x) = ? (k=0 to ?) x^k, for |x| < 1, to find the power series representation for the following function (centered at 0). Give the interval of convergence of the new series. f(10x) = 1 / (1 - 10x) Which of the following is the power series representation for f(10x)? A. ? (k=0 to ?) 1 / (1 - (10x)^k) B. ? (k=0 to ?) x^(10k) C. ? (k=0 to ?) 10x^k D. ? (k=0 to ?) (10x)^k The interval of convergence is [ ]. (Simplify your answer. Type your answer in interval notation.)

          Use the geometric series f(x) = 1 / (1 - x) = ? (k=0 to ?) x^k, for |x| < 1, to find the power series representation for the following function (centered at 0). Give the interval of convergence of the new series.

f(10x) = 1 / (1 - 10x)

Which of the following is the power series representation for f(10x)?

A. ? (k=0 to ?) 1 / (1 - (10x)^k)
B. ? (k=0 to ?) x^(10k)
C. ? (k=0 to ?) 10x^k
D. ? (k=0 to ?) (10x)^k

The interval of convergence is [ ].
(Simplify your answer. Type your answer in interval notation.)

Use the geometric series f(x) = 1 / (1 - x) = ? (k=0 to ?) x^k, for |x| < 1, to find the power series representation for the following function (centered at 0). Give the interval of convergence of the new series.

f(10x) = 1 / (1 - 10x)

Which of the following is the power series representation for f(10x)?

A. ? (k=0 to ?) 1 / (1 - (10x)^k)
B. ? (k=0 to ?) x^(10k)
C. ? (k=0 to ?) 10x^k
D. ? (k=0 to ?) (10x)^k

The interval of convergence is [ ].
(Simplify your answer. Type your answer in interval notation.)

Added by Nicol-S G.

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