Perhaps an alternative method would clear up the confusion. Since they are a geometric they differ by a multiplicative constant, lets call it . That is,
So and
therefore
Hope this helps.
Question :
If a,b,c are in Geometric Progression , prove that (1/a+b)+(1/b+c) = (1/b) .
I found that b^2=ac , and thus c = (b^2)/a and a = (b^2)/c here .
I managed to solve this problem , by substituting "c" in the equation as , (b^2)/a , and simplifying , after which the left hand side finally equated to 1/b.
I ran into a doubt , why do I need to substitute only for "c" in the equation to equate ? Why cant one substitute for both "a" , "c" or "a" , "c" , "b" simultaneously ?
I found that , once I substitute for more than once variable in the equation , the equation no longer equates . This maybe a stupid doubt , but please help me clear that abstract gap in my mind .
Thanks so much .
Hello, dagamer!
Can anyone explain the derivation for terms of a GP?
(And, if possible, for infinite terms, too?)
. . .We have: . . . . . . .[1]
Multiply by .[2]
Subtract [2] from [1]: .
. . Therefore: .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
For an infinite series . . .
. . .We have: . . . [1]
Multiply by . .[2]
Subtract [2] from [1]: .
. . Therefore: .