Question

calcule o sexto termo no desenvolvimento de (2x²-1/x³) elevado a 5

Answer 1

$\mathrm{(a+b)^n\ \to\ T_{p+1}=\binom{n}{p}.a^{n-p}.b^{p}}\\\\ \mathrm{\bigg(2x^2-\dfrac{1}{x^3}\bigg)^5\ \to\ p+1=6\ \to\ p=5}\\\\ \mathrm{T_{6}=T_{5+1}=\binom{5}{5}.(2x^2)^{5-5}.\bigg(\dfrac{-1}{x^3}\bigg)^{5}=}\\\\ \mathrm{=1.(2x^2)^0.\bigg(\dfrac{-1}{x^{15}}\bigg)=1.\bigg(\dfrac{-1}{x^{15}}\bigg)}\\\\ \boxed{\boxed{\mathbf{T_6=-\dfrac{1}{x^{15}}}}}$