Math  /  Algebra

Question6. What is the coefficient of 1/x61 / x^{6} in the expression (x5+1/x3)10\left(x^{5}+1 / x^{3}\right)^{10}.
ANS:

Studdy Solution
Calculate the coefficient of the desired term.
The coefficient is given by (107)\binom{10}{7}.
Calculate (107)\binom{10}{7}:
(107)=(103)=10×9×83×2×1=120 \binom{10}{7} = \binom{10}{3} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120
The coefficient of 1x6 \frac{1}{x^6} in the expression (x5+1/x3)10\left(x^{5}+1 / x^{3}\right)^{10} is 120 \boxed{120} .

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