We say that the infinite product II(1+ an) converges if the partial product PN II (1+ an) has a limit n=1 n=1 lim PN E (0, +∞); otherwise we say that it diverges. N00 Show that II(1+ an) converges if and only if In(1+an) converges. п-1 n=1 Hint: you need to use the continuity of e and In x!
We say that the infinite product II(1+ an) converges if the partial product PN II (1+ an) has a limit n=1 n=1 lim PN E (0, +∞); otherwise we say that it diverges. N00 Show that II(1+ an) converges if and only if In(1+an) converges. п-1 n=1 Hint: you need to use the continuity of e and In x!
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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We say that the infinite product I(1+ an) converges if the partial product Py = II (1+ an) has a limit
n=1
n=1
lim Py E (0,+∞); otherwise we say that it diverges.
Show that 1I(1+ an) converges if and only if In(1+ an) converges.
n=1
n=1
Hint: you need to use the continuity of e and In x!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F80d94f26-78c2-4200-b7e9-a2d0edad5216%2Faf9dc015-929a-4eb6-b6bc-b36d1a75dcbb%2Fry58aki_processed.png&w=3840&q=75)
Transcribed Image Text:N
We say that the infinite product I(1+ an) converges if the partial product Py = II (1+ an) has a limit
n=1
n=1
lim Py E (0,+∞); otherwise we say that it diverges.
Show that 1I(1+ an) converges if and only if In(1+ an) converges.
n=1
n=1
Hint: you need to use the continuity of e and In x!
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