- #1
kudzie adore
- 2
- 0
prove by Induction that n! ≥ 2^(n-1) n ≥ 1
Prove by Induction that n ≥ 2^(n-1) n ≥ 1
- Context: Graduate
- Thread starter kudzie adore
- Start date
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- Tags
- Induction
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Discussion Overview
The discussion revolves around proving the inequality n! ≥ 2^(n-1) for n ≥ 1 using mathematical induction. Participants explore the steps involved in the proof and seek assistance in completing the induction process.
Discussion Character
- Homework-related
- Mathematical reasoning
Main Points Raised
- One participant states they have proven the base case for n=1 and the inductive step for n=k, where k! ≥ 2^(k-1) is assumed to be true.
- The same participant expresses uncertainty about how to complete the proof for n=k+1, specifically questioning how to manipulate the inequality (k!)(k+1) ≥ 2^[(k+1)-1].
- Another participant offers a hint suggesting that if an equation is true, multiplying both sides by the same factor will maintain the truth of the equation.
Areas of Agreement / Disagreement
The discussion remains unresolved, with participants not reaching a consensus on the proof for n=k+1 and differing levels of understanding about the induction process.
Contextual Notes
Participants have not fully articulated the assumptions or definitions used in their proofs, and there are unresolved steps in the mathematical reasoning presented.
- #2
pwsnafu
Science Advisor
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Okay, so show us what you have attempted.
- #3
kudzie adore
- 2
- 0
I managed to prove for n= 1 and is true
for n=k k!≥ 2^ (k-1) and I assumed that n=k to be true
then for n= k+1 its (k+1)! ≥ 2^[(k+1)-1]
proof for n=(k+1)
(k!)(k+1) ≥ _____?
the problem is that how do we reach the proof for (k+1)
for n=k k!≥ 2^ (k-1) and I assumed that n=k to be true
then for n= k+1 its (k+1)! ≥ 2^[(k+1)-1]
proof for n=(k+1)
(k!)(k+1) ≥ _____?
the problem is that how do we reach the proof for (k+1)
- #4
tiny-tim
Science Advisor
Homework Helper
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hi kudzie adore! welcome to pf! 
(try using the X2 button just above the Reply box
)
hint: if an equation is true, then multiplying both sides by the same factor will still be true
(try using the X2 button just above the Reply box
)hint: if an equation is true, then multiplying both sides by the same factor will still be true
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