Question

A= \(\dfrac{1}{\sqrt{2}}+\left(\dfrac{1}{\sqrt{2}}\right)^2+\left(\dfrac{1}{\sqrt{2}}\right)^3+...+\left(\dfrac{1}{\sqrt{2}}\right)^{99}\)

Mọi người làm giúp mình bài 2 với ạ

Mình c.onn

Answer 1

\(u_1=\dfrac{1}{\sqrt{2}};q=\dfrac{1}{\sqrt{2}}\)

\(S_{99}=\dfrac{\dfrac{1}{\sqrt{2}}\cdot\left(\dfrac{1}{\sqrt{2}}^{99}-1\right)}{\dfrac{1}{\sqrt{2}}-1}=\dfrac{1}{\sqrt{2}}\cdot\left(\dfrac{1-2^{49}\cdot\sqrt{2}}{2^{49}\cdot\sqrt{2}}\right):\dfrac{1-\sqrt{2}}{\sqrt{2}}\)

\(=\dfrac{1}{1-\sqrt{2}}\cdot\dfrac{1-2^{49}\cdot\sqrt{2}}{2^{49}\cdot\sqrt{2}}\)