SOLUTION: if a, b, c, d are in continued proportion, prove that a^3 + b^3 + c^3 : b^3 + c^3 + d^3 = a : d.

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Question 1035971: if a, b, c, d are in continued proportion, prove that a^3 + b^3 + c^3 : b^3 + c^3 + d^3 = a : d.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
a, b, c, d in continued proportion ==> a/b = b/c = c/d = k for some constant of proportionality k
==> a+=+bk+=+ck%5E2+=+dk%5E3
==> b+=+a%281%2Fk%29, c+=+a%281%2Fk%29%5E2, and d+=+a%281%2Fk%29%5E3, and so a,b,c, and d form a geometric sequence.
==>.
BUT, a+=+dk%5E3, and so k%5E3+=+a%2Fd, and the statement is proved.