() 2k = 3", Vn E N k k=0 k n+1 Σ 2 Vn E N, n > 1 3 k=2 į * () 主) n 3k = 4", Vn E N %3D k k=0 = 2"-1, wheren is even 2k k=0 = 5", Vn E N k k=0 CIN

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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Question

Prove the following using mathematical induction.

()
n
11. 2*
= 3", Vn E N
k
k=0
k
12. E
2
n+1
,Vn E N, n> 1
3
k=2
()
= 4", Vn E N
k
13. У 3к
%3D
k=0
14.
2"-1, where n is even
2k
k=0
15. E
タ4
= 5", Vn E N
%3D
k
k=0
Transcribed Image Text:() n 11. 2* = 3", Vn E N k k=0 k 12. E 2 n+1 ,Vn E N, n> 1 3 k=2 () = 4", Vn E N k 13. У 3к %3D k=0 14. 2"-1, where n is even 2k k=0 15. E タ4 = 5", Vn E N %3D k k=0
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