Use mathematical induction to prove the statement is true for every positive integer n. 4+8+12+ + 4n = 2n(n+1) What is the first step in a mathematical induction proof? O Show that Sk + 1 is true. Show that S is true. Show that S₁ is true. Show that So is true. Let S be the statement 4 + 8 + 12 + ... +4n = 2n(n+1). Write the statement S₁. S₁: =(Do not simplify.) Simplify S, on the right. S₁:4= Is S₁ a true statement? Yes O No What is the next step in the proof? Show that if Sk + 1 is true, then Sk is true. Show that if S is true, then Sk+1 is true. Show that Sk is true. Show that Sk+ 1 is true. C
Use mathematical induction to prove the statement is true for every positive integer n. 4+8+12+ + 4n = 2n(n+1) What is the first step in a mathematical induction proof? O Show that Sk + 1 is true. Show that S is true. Show that S₁ is true. Show that So is true. Let S be the statement 4 + 8 + 12 + ... +4n = 2n(n+1). Write the statement S₁. S₁: =(Do not simplify.) Simplify S, on the right. S₁:4= Is S₁ a true statement? Yes O No What is the next step in the proof? Show that if Sk + 1 is true, then Sk is true. Show that if S is true, then Sk+1 is true. Show that Sk is true. Show that Sk+ 1 is true. C
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Use mathematical induction to prove the statement is true for every positive integer n.
4 +8+12+
+ 4n = 2n(n+1)
...
What is the first step in a mathematical induction proof?
Show that Sk +1 is true.
Show that Sk is true.
Show that S₁ is true.
Show that So is true.
Let S be the statement 4 + 8 + 12 + ... + 4n = 2n(n + 1). Write the statement S₁.
n
S₁:
(Do not simplify.)
Simplify S₁ on the right.
S₁: 4 =
Is S₁ a true statement?
1
Yes
No
What is the next step in the proof?
Show that if Sk+1
is true, then Sk is true.
Show that if Sk is true, then Sk+1 is true.
Show that Sk is true.
Show that Sk+1
is true.
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