using the binomial theorem to set up an equation

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eleven

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Jul 20, 2020
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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.
 
eleven said:
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.
Click to expand...
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 follow the rules of posting in this forum, as enunciated at:​
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Please share your work/thoughts about this assignment.​
 
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.
 
eleven said:
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.
Click to expand...
Very well then - please write out the first 4 terms of the binomial expansion of (x^2 +1.2)^n
 
eleven said:
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.
Click to expand...
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
 
I left it out cause I couldn't find the symbols, but I guess the two formulae are the same.
 
eleven said:
I left it out cause I couldn't find the symbols, but I guess the two formulae are the same.
Click to expand...
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 \(n\).
 
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.
 
eleven said:
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.
Click to expand...
1670698910460.png
 
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