Can anyone help me find the sixth term of $\displaystyle \left( x - \frac{1}{2}\right)^{10} ?$
Thanks.
A quick way (and probably the simplest way) is to apply the Binomial Theorem. To find the m-th term of a binomial with first term "a", second term "b", and power "n", use:
. . . . .$\displaystyle \frac{n!}{m!(n\, -\, m)!}\, a^{n-m} b^{m}$
Note: Remember to count the first term as "m = 0", so "the sixth term" is really "m = 5".
. . . . .$\displaystyle \frac{10!}{5!(10\, -\, 5)!}\,\left( x^{10-5} \right) \left(-\frac{1}{2}\right)^{5}$