I went to see a film with my friend Kitty y    ．The name of the film was S    ．It was a     a pretty p    ，her stepmother(继母)and a handsome prince．We bought the t    from the Internet．The film was very i    ．

将边长为1的正方形纸片按图1进行二等分分割，其阴影图形面积为S₁，继续将图2剩下空白部分二等分分割的图形面积为S₂，…，按此方法如图3第n次分割后得到的图形面积为S_n，求S₁+S₂+S₃+…+S_n=____．