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Find the term which does not contain x in the expansion for
Solution:
Consider the formula in getting the value of rth term
In this problem, we need only x and y in order to solve for the value of r where x in not involve in the binomial expansion. If x is not involve in the binomial expansion, then the exponent of x is 0. Any number (except zero) raised to zero power is always equal to one.
Since we need the exponents of x in order to solve for the value of r, then we can omit y and 2 as follows
Take the logarithm on both sides of the equation to the base x, we have
Therefore, there's no x at the 3rd term.Consider again the formula in getting the value of rth term
Substitute the values of n, r, x, and y in order to get the value at the 3rd term, we have
