(1) an+2−an+1=An+1a_{n+2} - a_{n+1} = A_{n+1}an+2−an+1=An+1 an+1−an=Ana_{n+1} - a_n = A_nan+1−an=An とおくと An+1=2AnA_{n+1} = 2A_nAn+1=2An 初項 A1=a2−a1=1−0=1A_1 = a_2 - a_1 = 1 - 0 = 1A1=a2−a1=1−0=1、公比 r=2r = 2r=2 なので An=1⋅2n−1=2n−1A_n = 1 \cdot 2^{n-1} = 2^{n-1}An=1⋅2n−1=2n−1 (2) (1)より an+1−an=2n−1a_{n+1} - a_n = 2^{n-1}an+1−an=2n−1 a1=0a_1 = 0a1=0 、 a2=1a_2 = 1a2=1 、 a3=3a_3 = 3a3=3 、 a4=7a_4 = 7a4=7 、・・・ となるので an=2n−1−1a_n = 2^{n-1} - 1an=2n−1−1