Question

(-3/2)^2+(-3/2)^3 +(-3/2)^4+(-3/2)^5+...+(-3/2)^100

Answer 1

\(A=\left(-\dfrac{3}{2}\right)^2+\left(-\dfrac{3}{2}\right)^3+...+\left(-\dfrac{3}{2}\right)^{100}\)

=>\(\dfrac{-3}{2}\cdot A=\left(-\dfrac{3}{2}\right)^3+\left(-\dfrac{3}{2}\right)^4+...+\left(-\dfrac{3}{2}\right)^{101}\)

=>\(\dfrac{-5}{2}\cdot A=\left(-\dfrac{3}{2}\right)^{101}-\left(-\dfrac{3}{2}\right)^2\)

\(\Leftrightarrow A=\left[\left(-\dfrac{3}{2}\right)^{101}-\left(-\dfrac{3}{2}\right)^2\right]\cdot\dfrac{-2}{5}\)