Using the binomial expansion n (1 + x)² = ± (1) x², k=0 prove the following relations n n ()-()+()-() (7) - (?) + (²3) (13) - (7) + + = = 2n/2 :(¹7), 4 COS 20/2 sin(). where in each case the sum includes terms up to (m) satisfying m ≤ n. Check your results by computing both sides of both equations in the case n = 5.

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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Using the binomial expansion
n
(1 + x)² = ± (1) x²,
k=0
prove the following relations
n
()-()+()-(6)
(1)- (3) + (3)
(3) - (7)
+
+
=
=
2n/2
COS
(¹27),
4
2n/2 sin
¹(¹7),
where in each case the sum includes terms up to (m) satisfying m ≤ n.
Check your results by computing both sides of both equations in the case n = 5.
Transcribed Image Text:Using the binomial expansion n (1 + x)² = ± (1) x², k=0 prove the following relations n ()-()+()-(6) (1)- (3) + (3) (3) - (7) + + = = 2n/2 COS (¹27), 4 2n/2 sin ¹(¹7), where in each case the sum includes terms up to (m) satisfying m ≤ n. Check your results by computing both sides of both equations in the case n = 5.
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