→ a88241050 :10-1=9=公比^n, S3n/Sn=公比^2n+公比^n+1=91 04/14 16:29
→ suker :如果不會帶數字(偷懶) 1 9 81, s1=1,s2=10,s3=91 04/14 16:43
→ ckchi :實在不行就回到最原始 04/15 10:29
→ ckchi :Sn = a[r^n-1]/r-1 04/15 10:30
→ ckchi :S2n = a[r^(2n)-1]/r-1 04/15 10:30
→ ckchi :S2n = a[r^(3n)-1]/r-1 04/15 10:30
→ ckchi :所以... 04/15 10:30
→ ckchi :S2n/Sn = [r^(2n)-1] / [r^n-1] = 10 04/15 10:30
→ ckchi : => r^(2n)-1 = 10*(r^n-1) 04/15 10:30
→ ckchi : => (r^n)^2 -10*(r^n) +9 = 0 04/15 10:30
→ ckchi : => r^n = 9 or 1(分母會變0，不合) 04/15 10:30
→ ckchi :因此... 04/15 10:33
→ ckchi :S3n/Sn = [r^(3n)-1] / [r^n-1] 04/15 10:33
→ ckchi : = [(r^n)^3 - 1] / [r^n-1] 04/15 10:33
→ ckchi : = (729-1) / (9-1) 04/15 10:34
→ ckchi : = 728/8 = 9 04/15 10:34
→ ckchi :91... 1沒打到 04/15 10:34
→ ckchi :.. 第4行要改 S"3"n = a[r^(3n)-1]/r-1 04/15 10:36
→ sneak : //muxiv.com 11/10 11:39