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

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 92E
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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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