Induction Inequality Proof: 3^n is greater than or equal to 2n + 1
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- เผยแพร่เมื่อ 2 ต.ค. 2024
- Induction Inequality Proof: 3^n is greater than or equal to 2n + 1
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Thank you:)
![Prove that 11^n - 4^n is divisible by 7 for any natural number, n. [Mathematical Induction]](http://i.ytimg.com/vi/pLbG3Vvpjjk/mqdefault.jpg)
i am so confused as to how and why inequality sign changed mid calculations.
since 3^k is already >= , it would make sense that 3^(k+1)> . If K is greater then, then k+1 is definitely greater. While if K is equal to, then k+1 would also be greater, if this is what you ment.
Sir, I am literally thankful of this channel and your existence. Thank you!
😂
can you show 3(2k + 2 + 1) by adding values to left side (this should be ok because it's greater than) and then simply say 3(2k + 2 + 1) is greater than 2(k + 1) + 1 because our domain is positive integers and the same equation * 3 is greater than the one that's not
You must used
(1+x)^n>=1+nx
n€IN and x€IR+
ur thumbnail is different from the proof u do btw lool
omg! I will fix it, thank you!!!!!!!!!!!!!!!!!!!!!
Thank you so much Sir . This video is really very helpful for me.
Thank the lord this video found me, you saved me hours of pain yet again!
inequality n² ≤ 9 = 0,1,2 and 3 I know is -1, -2 and -3 but can someone explain it why or show me step by step
can the base case be 0 that 3^0 = 1?
Natural numbers start from 1 not zero
VERY WELL SIMPLIFIED. THANK YOU SIR
6:42 the explanation for this makes no sense, you kept the multiplication of 3*1 in 2k+3 but you're free to throw away 3x2k? Where did it go? Why is one okay without the other?
it's not an equation, he's showing that (3 * 2k + 3) > (2k + 3)
For example, 3a > a when a is Z+.
thank you, i didn't get that part