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mathematical induction; please help me

Proof that $left(sum^n_{k=1}x_kright)left(sum^n_{k=1}y_kright)geq n^2$Mathematical Induction Proof 1Using mathematical induction to show that for any $nge 2$ then $prod_{i=2}^nbigl(1-frac{1}{i^2}bigr)=frac{n+1}{2 n}$Mathematical Induction Proof Question dealing with integersCan't prove $2^n > n$ with Mathematical InductionUse strong induction to prove the ones digit of 4^k.Proof by induction, factorials and exponentsBasic mathematical induction question.Use mathematical induction to proveI'm stuck on this mathematical induction problem

-1

$begingroup$

I've been stuck on this problem for hours; I have no idea how to even calculate it. If anyone can help me break it down step-by-step, I would truly appreciate it. Here's the problem:

for every natural number $n$, prove that
$$ (a+b)^n = a^n + C_{1}^{n} a^{n-1} b + C_{2}^{n} a^{n-2} b^n + ... C_{n}^{n-1} a b^{n-1} + b^n. $$

induction

share|cite|improve this question

edited 16 hours ago

Javi

3,0212832

asked Mar 13 at 23:27

Muiz GhifariMuiz Ghifari

12

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  $begingroup$
  Welcome to stackexchange. We can't help unless you edit the question to provide more information. You can start somewhere: write down and show that you understand the definition of $C_k^n$. Then write down and verify that equation for $n=1$ and $n=2$ and $n=3$ and $n=4$. See if you can see a way to get the expression for $n=4$ from that for $n=3$.
  $endgroup$
  – Ethan Bolker
  Mar 13 at 23:33
  
  
  

  
  
  
  


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  This is a rather advanced exercise in basic induction. If you don't know induction, as you said in a past question, don't even attempt to this before you've managed to solve simpler questions.
  $endgroup$
  – DonAntonio
  Mar 13 at 23:42
  

  
  
  
  


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  @EthanBolker my teacher said using lesson calculus
  $endgroup$
  – Muiz Ghifari
  Mar 13 at 23:45
  

  
  
  
  


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  What you need to show is that $(a+b)(a+b)^n$ has the correct form assuming $(a+b)^n$ has the correct form.
  $endgroup$
  – herb steinberg
  Mar 13 at 23:45
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @herbsteinberg why?
  $endgroup$
  – Muiz Ghifari
  Mar 13 at 23:47
  

  
  
  
  

 | 
show 6 more comments

-1

$begingroup$

I've been stuck on this problem for hours; I have no idea how to even calculate it. If anyone can help me break it down step-by-step, I would truly appreciate it. Here's the problem:

for every natural number $n$, prove that
$$ (a+b)^n = a^n + C_{1}^{n} a^{n-1} b + C_{2}^{n} a^{n-2} b^n + ... C_{n}^{n-1} a b^{n-1} + b^n. $$

induction

share|cite|improve this question

edited 16 hours ago

Javi

3,0212832

asked Mar 13 at 23:27

Muiz GhifariMuiz Ghifari

12

$endgroup$

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome to stackexchange. We can't help unless you edit the question to provide more information. You can start somewhere: write down and show that you understand the definition of $C_k^n$. Then write down and verify that equation for $n=1$ and $n=2$ and $n=3$ and $n=4$. See if you can see a way to get the expression for $n=4$ from that for $n=3$.
  $endgroup$
  – Ethan Bolker
  Mar 13 at 23:33
  
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  This is a rather advanced exercise in basic induction. If you don't know induction, as you said in a past question, don't even attempt to this before you've managed to solve simpler questions.
  $endgroup$
  – DonAntonio
  Mar 13 at 23:42
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @EthanBolker my teacher said using lesson calculus
  $endgroup$
  – Muiz Ghifari
  Mar 13 at 23:45
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  What you need to show is that $(a+b)(a+b)^n$ has the correct form assuming $(a+b)^n$ has the correct form.
  $endgroup$
  – herb steinberg
  Mar 13 at 23:45
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @herbsteinberg why?
  $endgroup$
  – Muiz Ghifari
  Mar 13 at 23:47
  

  
  
  
  

 | 
show 6 more comments

$begingroup$

I've been stuck on this problem for hours; I have no idea how to even calculate it. If anyone can help me break it down step-by-step, I would truly appreciate it. Here's the problem:

for every natural number $n$, prove that
$$ (a+b)^n = a^n + C_{1}^{n} a^{n-1} b + C_{2}^{n} a^{n-2} b^n + ... C_{n}^{n-1} a b^{n-1} + b^n. $$

induction

share|cite|improve this question

edited 16 hours ago

Javi

3,0212832

asked Mar 13 at 23:27

Muiz GhifariMuiz Ghifari

12

$endgroup$

share|cite|improve this question

edited 16 hours ago

Javi

3,0212832

asked Mar 13 at 23:27

Muiz GhifariMuiz Ghifari

12

share|cite|improve this question

edited 16 hours ago

Javi

3,0212832

asked Mar 13 at 23:27

Muiz GhifariMuiz Ghifari

12

edited 16 hours ago

Javi

3,0212832

edited 16 hours ago

Javi

3,0212832

asked Mar 13 at 23:27

Muiz GhifariMuiz Ghifari

12

asked Mar 13 at 23:27

Muiz GhifariMuiz Ghifari

12