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a1+a2+a3+a4+...............an is an A.P. prove that 1/a1*an+1/a2*an-1+1/a3*an-2.........+1/an*a1= 2/a1+an*(1/a1+1/a2+1/a3.........1/an)

a1+a2+a3+a4+...............an is an A.P. prove that 1/a1*an+1/a2*an-1+1/a3*an-2.........+1/an*a1= 2/a1+an*(1/a1+1/a2+1/a3.........1/an)
 

Grade:10

1 Answers

Harsh Patodia IIT Roorkee
askIITians Faculty 907 Points
8 years ago
use
​a2-a1 = a3-a2 = a4-a3 . . . . = an- an-1 =d say
a2-a1 =d divide by a1a2 1/a1 + ​1/a2 = d/a1a2
a3-a2= d divide by a2a3 1/a2 + 1/a3 = d/a2a3
Similarly proceed and add. You will get the required result.

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