Binomial expansion: 2 Questions

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M4STR0k

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A) According to the ascending powers of x in the expansion of (1+x)^n if t3=28x^2 , T5= 1120 find n and x

B) In the expansion of (1+x)^n if the coefficient of t6 = coefficient of t10 then find n


Hint for those pls
 
M4STR0k said:
A) According to the ascending powers of x in the expansion of (1+x)^n if t3=28x^2 , T5= 1120 find n and x

B) In the expansion of (1+x)^n if the coefficient of t6 = coefficient of t10 then find n


Hint for those pls
Click to expand...

What is the third term of expansion (descending power of x) for (1+ x)n?
 
M4STR0k said:
A) According to the ascending powers of x in the expansion of (1+x)^n if t3=28x^2 , T5= 1120 find n and x

B) In the expansion of (1+x)^n if the coefficient of t6 = coefficient of t10 then find n


Hint for those pls
Click to expand...
A) To find n:

Ascending powers of x:

\(\displaystyle (1+x)^n= 1+nC1 x + nC2 x^2 + nC3 x^3 +nC4 x^4 + ...\)

\(\displaystyle t3 = nC2 x^2 = 28 x^2\)

So \(\displaystyle nC2 = 28\)

Now \(\displaystyle nC2 = n(n-1)/2 = 28\)

You can take it from there.

To find x:
Take n=? from above, substitute it in for n in t5 in expansion above , equate to 1120 and solve for x.

B) You need to know that \(\displaystyle nCr =nCn-r \) .... (the reason why Pascal's triangle reads the same right to left as left to right).
 
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