- #1
icystrike
- 445
- 1
Homework Statement
Find the coefficient of [tex]x^{29}[/tex] in the expansion of [tex](1+x^{5}+x^{7}+x^{9})[/tex].
CompuChip said:It is zero: there is no [itex]x^{29}[/itex] term in
[tex]
(1+x^{5}+x^{7}+x^{9})
[/tex]
I suppose you are missing some power?
The formula for binomial expansion is (a + b)^n = ∑(nCr)a^(n-r)b^r, where a and b are constants, n is the power, and nCr is the combination formula for choosing r objects from a set of n objects.
To find the coefficient of a specific term, you can use the combination formula (nCr) and the exponent of the term. The coefficient of a term with the exponent k can be calculated as nCk, where n is the power and k is the exponent of the term.
Binomial expansion can be applied in various real-life situations, such as in finance for calculating compound interest, in probability for calculating the chances of an event occurring multiple times, and in genetics for predicting the inheritance of traits.
The coefficient of a term in binomial expansion represents the number of ways that term can be obtained from the expansion. It also indicates the relative importance or weight of that term in the overall expansion.
To expand a binomial to a certain power, you can use the formula (a + b)^n = ∑(nCr)a^(n-r)b^r, where a and b are the constants in the binomial and n is the desired power. Then, you can use the combination formula (nCr) to calculate the coefficients of each term in the expansion.