等比數列和公式證明

Question

Sn=a1（r^n-1）/ r-1，（r>1），該如何證明這個公式？請寫的越詳細越好，感謝您 ^^

Answer 1

證明 Sn = a1＋(rn-1)/( r-1), (r > 1)
Sn = a1＋a1*r＋a1*r2＋a1*r3＋...＋a1*rn-1 ... (1)
r*Sn = a1*r＋a1*r2＋a1*r3＋a1*r4＋...＋a1*rn ... (2)
(2) - (1) = (r-1)*Sn = a1*rn - a1= a1*(rn - 1)
=> Sn = a1＋(rn-1)/( r-1)
如果有問題, 請來函討論. 不然, 我可能會錯失你再補充的疑點.