Suppose you want to use mathematical induction to prove that 1 + 2 + 2² +23³ +.... +2 = 2n+1 - 1 for all positive integers n. Which of these is the correct statement to be proved in the basis step?
Suppose you want to use mathematical induction to prove that 1 + 2 + 2² +23³ +.... +2 = 2n+1 - 1 for all positive integers n. Which of these is the correct statement to be proved in the basis step?
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 + 2² +23³ +....
+2n = 2n+1 -1
for all positive integers n. Which of these is the correct statement to be proved in the basis step?
01+ 2+22 +23+...+2k = 2k+1 - 1
1+2¹= 2¹+1 -1
20+1 -1
01+ 2+22² +2³+...+2 = 2n+1 − 1
01=20+1 -1
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