# If the #p^(th), q^(th), and r^(th)# of a H.P is a,b,c respectively, then prove that#(q-r) /a + (r-p) / b + (p-q)/c = 0#?

##### 1 Answer

Aug 21, 2017

Please see below.

#### Explanation:

Before we commence with the question, two things first.

- If
#a_m# and#a_n# are#m^(th)# and#n^(th)# terms of an Arithmetic Progression, whose**common difference is**#d# , then#a_m-a_n=(m-n)d# . - If
#h_1,h_2,h_3,h_4,.....# are in H.P., then#1/h_1,1/h_2,1/h_3,1/h_4,.....# are in A.P.

Hence, as

or **......................(1)**

Similarly **......................(2)**

and **......................(3)**

Hence

=

=

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