using the binomial theorem to set up an equation

[eleven]

Hi
I need help solving the following question:
Consider the expansion of (x^2 +1.2)^n where n∈ Z, n ≥ 3. Given that the coefficient of the
term containing x^6 is greater than 200 000 , find the smallest possible value of n.

The solution is supposed to be n=27.

 

[Deleted member 4993]

Hi
I need help solving the following question:
Consider the expansion of (x^2 +1.2)^n where n∈ Z, n ≥ 3. Given that the coefficient of the
term containing x^6 is greater than 200 000 , find the smallest possible value of n.

The solution is supposed to be n=27.

Can you write the binomial expansion of (a+x)ⁿ?

Please show us what you have tried and exactly where you are stuck.​

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Please share your work/thoughts about this assignment.​

 

[eleven]

Yes, I know how to use the formula. I tried to look at the mark scheme, but it doesn't explain very well. It says that r=3, but I can't understand why that's correct.

 

[Deleted member 4993]

Yes, I know how to use the formula. I tried to look at the mark scheme, but it doesn't explain very well. It says that r=3, but I can't understand why that's correct.

Very well then - please write out the first 4 terms of the binomial expansion of (x^2 +1.2)^n

 

[pka]

Yes, I know how to use the formula. I tried to look at the mark scheme, but it doesn't explain very well. It says that r=3, but I can't understand why that's correct.

If you really know then this is ole hat to you.
${\left( {{x^2} + 1.2} \right)^n} = \sum\limits_{k = 0}^n {\dbinom{n}{k}{x^{2k}}{{(1.2)}^{n - k}}}$ We want the coefficient of $x^6$.
Therefore in the sum $k=3$. So we need $n$ so that \(\left( {\begin{array}{*{20}{c}} n \\ 3 \end{array}} \right){(1.2)^{n - 3}} \geqslant 2 \cdot {10^5}\)

Look HERE

 

[eleven]

Why is it not (x^2)^(n-k)*(1.2)^k ?

 

[pka]

Why is it not (x^2)^(n-k)*(1.2)^k ?

Well where is the rest of the binomial coefficient?

 

[eleven]

I left it out cause I couldn't find the symbols, but I guess the two formulae are the same.

 

[pka]

I left it out cause I couldn't find the symbols, but I guess the two formulae are the same.

Pardon me, but that is a silly answer. The focus is on $x^6=(x^2)^k$
Solve this: \(\left( {\begin{array}{*{20}{c}} n \\ 3 \end{array}} \right){(1.2)^{n - 3}} \geqslant 2 \cdot {10^5}\) for least $n$.

 

[eleven]

Thank you for the help. It makes more sense to me now.

 

[eleven]

Btw; where do you find all those math symbols? It's a little hard to show my working here cause the keyboard doesn't have all the math symbols I need.

 

[nasereid]

Hi
I need help solving the following question:
Consider the expansion of (x^2 +1.2)^n where n∈ Z, n ≥ 3. Given that the coefficient of the
term containing x^6 is greater than 200 000 , find the smallest possible value of n.

The solution is supposed to be n=27.