標題:
A.S AND G.S.
發問:
if a and b are positive real numbers, (a) show that the sequence log a , log ab , log ab^2 , log ab^3 , ... is an arithmetic sequence (b) and hence find its general term
最佳解答:
(a) log a=log a log ab= log a+log b log ab^2=log a+log b^2 =log a+2 log b log ab^3=log a+ log b^3 =log a + 3log b log ab^3-log ab^2 =log b log ab^2-log ab=log b log ab- log a=log b so log a , log ab , log ab^2 , log ab^3 , ... is an arithmetic sequence (b) T(n)=a+nd = log a+n(log b) =log a + log b^n =log ab^n so the general term T(n)=log ab^n
A.S AND G.S.
發問:
if a and b are positive real numbers, (a) show that the sequence log a , log ab , log ab^2 , log ab^3 , ... is an arithmetic sequence (b) and hence find its general term
最佳解答:
(a) log a=log a log ab= log a+log b log ab^2=log a+log b^2 =log a+2 log b log ab^3=log a+ log b^3 =log a + 3log b log ab^3-log ab^2 =log b log ab^2-log ab=log b log ab- log a=log b so log a , log ab , log ab^2 , log ab^3 , ... is an arithmetic sequence (b) T(n)=a+nd = log a+n(log b) =log a + log b^n =log ab^n so the general term T(n)=log ab^n
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