Using induction, please prove the following: (a) For all n € Z+, (b) For all n = Z+, n Σ(−1)²¡² – (-1)″n(n+1) 2 i=1 n Σ 1 i(i+1) = n n+1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Using induction, please prove the following:
(a) For all n € Z+,
(b) For all n = Z+,
n
Σ(−1)²¡² – (-1)″n(n+1)
2
i=1
n
Σ
1
i(i+1)
=
n
n+1
Transcribed Image Text:Using induction, please prove the following: (a) For all n € Z+, (b) For all n = Z+, n Σ(−1)²¡² – (-1)″n(n+1) 2 i=1 n Σ 1 i(i+1) = n n+1
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