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Prove that if n is odd then 3n+ 7 is even. Show that if n is an odd prime number it is not necessarily true that n + 2 is prime. Prove by induction that 6r = 3n(n+1) r=0 Find Tn and Sn for the series 5+7+9+... Prove by induction that

Prove that if n is odd then 3n+ 7 is even. Show that if n is an odd prime number it is not necessarily true that n + 2 is prime. Prove by induction that 6r = 3n(n+1) r=0 Find Tn and Sn for the series 5+7+9+... Prove by induction that

Advanced Engineering Mathematics
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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Prove that if n is odd then 3n + 7 is even. Show that if n is an odd prime number it is not necessarily true that n + 2 is prime. Prove by induction that n Σ6r= 3n(n+1) r=0 Find Tn and Sn for the series 5+7+9+... Prove by induction that n (2r +1) = n(n + 2) . Use the method of induction to prove that n 3" = Find the first four terms of the series defined by n r=1 n 3(3¹ - 1) 2 r=1 . Use induction to prove that 5n(n+1) 2 5r= 5r
Transcribed Image Text:Prove that if n is odd then 3n + 7 is even. Show that if n is an odd prime number it is not necessarily true that n + 2 is prime. Prove by induction that n Σ6r= 3n(n+1) r=0 Find Tn and Sn for the series 5+7+9+... Prove by induction that n (2r +1) = n(n + 2) . Use the method of induction to prove that n 3" = Find the first four terms of the series defined by n r=1 n 3(3¹ - 1) 2 r=1 . Use induction to prove that 5n(n+1) 2 5r= 5r
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