If a,x,y,z,b are in Harmonic progression,, can 1/x be equal to (3/4a)+(1/4b)?If yes,how?
回答 (2)
2015-09-07 5:16 pm
a,x,y,z,b are in harmonic progression, so,
1/a, 1/x, 1/y, 1/z, 1/b are in arithmetic progression.
Assume the n-th term of the arithmetic progression is given by
An = 1/a + (n-1)d
A5 = 1/a + 4d = 1/b
d = ( 1/b - 1/a )/4 = 1/(4b) - 1/(4a)
1/x
= A2
= 1/a + d
= 1/a + 1/(4b) - 1/(4a)
= 4/(4a) + 1/(4b) - 1/(4a)
= 3/(4a) + 1/(4b)
1/a, 1/x, 1/y, 1/z, 1/b are in arithmetic progression.
Assume the n-th term of the arithmetic progression is given by
An = 1/a + (n-1)d
A5 = 1/a + 4d = 1/b
d = ( 1/b - 1/a )/4 = 1/(4b) - 1/(4a)
1/x
= A2
= 1/a + d
= 1/a + 1/(4b) - 1/(4a)
= 4/(4a) + 1/(4b) - 1/(4a)
= 3/(4a) + 1/(4b)
收錄日期: 2021-05-02 14:05:47
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20150907084527AAFIYiS