Please help me!!

[Steven G]

I think that MarkFL meant to write 1+x and not 1-x.

 

[MarkFL]

why can it change (1 + x) to (1-x) ?

It was a typo...I've edited my post.

 

[MarkFL]

2. for every natural number n, prove that View attachment 11350 ?

This is the binomial theorem. I would state the induction hypothesis as:

[MATH](a+b)^n=\sum_{k=0}^n\left({n \choose k}a^{n-k}b^k\right)[/MATH]
Now, consider the following definition:

[MATH]{n \choose r}\equiv\frac{n!}{r!(n-r)!}[/MATH]
See if you can verify the following identities (which will prove useful for your proof by induction of the binomial theorem):

i) [MATH]{n \choose 0}=1[/MATH]
ii) [MATH]{n \choose n}=1[/MATH]
iii) [MATH]{n \choose r}={n \choose n-r}[/MATH]
iv) [MATH]{n \choose r}+{n \choose r-1}={n+1 \choose r}[/MATH]
Once you have shown your verification of these identities, we will be ready to begin the inductive proof.

 

[muiz205]

This is the binomial theorem. I would state the induction hypothesis as:

[MATH](a+b)^n=\sum_{k=0}^n\left({n \choose k}a^{n-k}b^k\right)[/MATH]
Now, consider the following definition:

[MATH]{n \choose r}\equiv\frac{n!}{r!(n-r)!}[/MATH]
See if you can verify the following identities (which will prove useful for your proof by induction of the binomial theorem):

i) [MATH]{n \choose 0}=1[/MATH]
ii) [MATH]{n \choose n}=1[/MATH]
iii) [MATH]{n \choose r}={n \choose n-r}[/MATH]
iv) [MATH]{n \choose r}+{n \choose r-1}={n+1 \choose r}[/MATH]
Once you have shown your verification of these identities, we will be ready to begin the inductive proof.

thanks prof