if the pth term of a hp is q and the qth term is p,prove that its (p+q)th term is pq/p+q

Asked by  | 15th Aug, 2012, 07:05: PM

Expert Answer:

Given,
Tp = q............ in HP
Tq = p............ in HP

Therefore, In AP
Tp = 1 / q
Tq = 1 / p

d = Tp - Tq / p - q
= (1 / q) - (1 / p) / p - q
= (p - q / pq) / p - q
Therefore, 
d = 1 / pq

Again,
Let Tp+q = X

d = Tp - Tp+q / p - ( p + q)
1 / pq = 1 / q - X / q
X = 1 / p + 1 / q
X = p + q / pq.............. in AP

Therefore, in HP, Tp+q = pq / p+q

Answered by  | 15th Aug, 2012, 10:28: PM

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