if x1,x2,x3 ....xn are in H.P then prove that x1x2+x2x3+x3x4+....+xn-1xn =( n-1)x1xn

given: are in HP.

therefore are in AP.

therefore let the common difference of the AP is d..

therefore

 ............(1)

similarly

..........(2)

and is the nth term of the AP series .

therefore

.............(3)

now the LHS part of the given equation is:

= RHS

hope this helps you.

cheers!!

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