29 Questions
What is the relation between the sum of coefficients of even terms and the sum of coefficients of odd terms in the expansion of (1+x)^n?
Sum of coefficients of even terms is equal to sum of coefficients of odd terms
What is the value of C_r in terms of C_(r-1) in the expansion of (1+x)^n?
C_r = (n-r+1)C_(r-1)/r
If (1+x)^n = C_0 + C_1x + C_2x^2 +... + C_nx^n, then what is the value of C_0 + C_1 + C_2 +... + C_n?
2^n
What is the sum of the product of coefficients in the expansion of (1+x)^n?
2^n
What is the coefficient of x^r in the expansion of (1+x)^n?
n!/(r!(n-r)!)
What is the total number of terms in the expansion of (x + y)^n?
n+1
If n Cr = n C(n - r), what can be concluded about the coefficients of consecutive terms in the expansion of (x + y)^n?
They are equidistant from the beginning and end
What is the sum of the powers of x and y in each term of the expansion of (x + y)^n?
n
What is the value of n Cr when r = 0?
1
What is the property of the binomial coefficients n Cr in the expansion of (x + y)^n?
They are equidistant from the beginning and end
If $a_1, a_2, a_3, a_4$ are the coefficients of any four consecutive terms in the expansion of $(1+x)^n$, then what is the value of $\frac{a_1}{a_3}+\frac{a_2}{a_4}$?
$\frac{n+1}{n-1}$
In the expansion of $(1+x)^n$, if $a_r$ is the coefficient of $x^{r-1}$, then what is the value of $\frac{a_r}{a_{r+2}}$?
$\frac{r+1}{n-r+1}$
In Pascal's Triangle, each entry is the sum of the two entries directly above it. What is the value of the sum of the reciprocals of all the binomial coefficients in the $(n+1)^{th}$ row?
$2$
If $a_1, a_2, a_3, a_4$ are the coefficients of any four consecutive terms in the expansion of $(1+x)^n$, then what is the value of $a_1a_3-a_2a_4$?
$0$
In the expansion of $(1+x)^n$, what is the value of the coefficient of $x^{n-2}$ in terms of $n$?
$\frac{n(n-1)}{2}$
What is the general term in the expansion of (x + y)^n?
n C_r x^(n - r) y^r
What is the independent term in the expansion of (x + y)^n?
n C_n y^0
What is the coefficient of the constant term in the expansion of (x + y)^n?
n C_n
What is the sum of the coefficients of the odd terms in the expansion of (x + y)^n?
2^n
What is the relation between the coefficients of the binomial expansion of (x + y)^n and (x - y)^n?
They are equal in magnitude but alternate in sign
What is the value of the middle term in the expansion of (1+x)^2n?
10 C5 x^5
If the middle term in the expansion of (1+x)^n is 10 C5 x^5, what is the value of n?
10
In the expansion of (x+y)^n, what is the value of the coefficient of the middle term?
n!/((n/2)!*(n/2)!)
What is the coefficient of x^r in the expansion of (1+x)^n?
n Cr
If the middle term in the expansion of (1+x)^n is T((n+1)/2), what is the value of T((n+1)/2) when n is odd?
n C((n+1)/2)
What is the condition for the validity of the expansion (1 + x)^n?
-1 < x < 1
What is the value of the coefficient of a^3b^4c^5 in the expansion of (bc + ca + ab)^6?
60
What is the value of n in the expansion (1 + x)^n when x is very small?
nx + 1
What is the number of terms in the series expansion of (1 + x)^n?
Infinite
Test your understanding of binomial expressions, binomial theorem, and expansions. Learn to expand powers of binomials and apply the binomial theorem to solve problems.
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