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kimjp56io5
08.04.2020 •
Mathematics
Suppose that the power series, LaTeX: \sum c_n x^n∑ c n x n, converges when x = −4 and diverges when x = 7. Determine whether each statement is true, false or not possible to determine. (a) The power series converges when x = 10. (b) The power series converges when x = 3. (c) The power series diverges when x = 1. (d) The power series diverges when x = 6.
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Ответ:
A. FALSE
B. TRUE
C. FALSE
D. NOT POSSIBLE TO DETERMINE
Step-by-step explanation:
(A) FALSE. since the power series ∑
has radius of convergence |-4|=4 ans 7> 4 which is beyond its radius of convergence. thus by the theorem of power series, the series diverges at 10.
(B)TRUE. since the radius of convergence of the power series ∑
must be at least |-4| = 4 and 3 lies within this radius, thus it converges at x=3
(C)FALSE the series does not diverge at x=1, since 1 is within its radius of convergence |-4| = 4
(D)NOT POSSIBLE TO DETERMINE
At x=6, it is beyond its radius of convergence but has not attain its divergence point. thus it is not possible to determine.
Ответ: