7. Show that 1 (1+x)(1+x²)... (1+x²") = for all x € R \ {1} and n € N. Then deduce the limit 2n+1 X² - X 3 5 22 lim (In+In+---+ In (²+¹) n→+∞ 22n
7. Show that 1 (1+x)(1+x²)... (1+x²") = for all x € R \ {1} and n € N. Then deduce the limit 2n+1 X² - X 3 5 22 lim (In+In+---+ In (²+¹) n→+∞ 22n
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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Transcribed Image Text:7. Show that
(1 + x) (1 + x²) …. (1 + x²”)
for all x € R \ {1} and n € N. Then deduce the limit
=
2n+1
1 X²
X -
3
5
22
lim (In+In+---+ In (²+¹)
n→+∞
22n
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