Suppose you want to use mathematical induction to prove that 1 + 2 +2² +2³+.... + 2n = 2n+1 -1 for all positive integers n. Which of these is the correct formulation of the induction step? O Show that 1+2= 2¹+1 -1 is true Show that 1= 20+1 - 1 is true Assume 1 + 2 +2² +2³+...+2k is true, and show that 1+ 2+2² +2³+ O Assume 2k+1 - 1 is true, and show that 2k+2 - 1 is true. Assume 1 + 2 + 2² +23+...+2 = 2k+1 -1 is true, and show that 1+ 2+2² +2³+...+2k+1 = 2k+2 -1 is true. +2²+1 is true.
Suppose you want to use mathematical induction to prove that 1 + 2 +2² +2³+.... + 2n = 2n+1 -1 for all positive integers n. Which of these is the correct formulation of the induction step? O Show that 1+2= 2¹+1 -1 is true Show that 1= 20+1 - 1 is true Assume 1 + 2 +2² +2³+...+2k is true, and show that 1+ 2+2² +2³+ O Assume 2k+1 - 1 is true, and show that 2k+2 - 1 is true. Assume 1 + 2 + 2² +23+...+2 = 2k+1 -1 is true, and show that 1+ 2+2² +2³+...+2k+1 = 2k+2 -1 is true. +2²+1 is true.
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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Transcribed Image Text:Suppose you want to use mathematical induction to prove that
1 + 2 +22² +23³ +... + 2 = 2n+1 - 1
for all positive integers n. Which of these is the correct formulation of the induction step?
O Show that 1+2 = 2¹+¹ 1 is true
Show that 1 = 20+1 -1 is true
Assume 1 + 2 +2² +2³+...+2k is true, and show that 1 + 2 + 22 +23+...+2+1 is true.
Assume 2k+1 - 1 is true, and show that 2k+2 -1 is true.
Assume 1 + 2 + 22 +23+...+2k = 2k+1 - 1 is true, and show that
1+ 2+2² +23+...+2k+1 = 2k+2 - 1 is true.
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