A beautiful Sum by DK

Just came across a beautiful question.....

If a₁, a₂, a₃, a₄ are in HP then

1a₁a₄\sum_{r=1}^{3}{}a_r a_r+1 is a root of :

A) x² + 2x + 15 = 0
B) x² + 2x - 15 = 0
C) x² - 2x + 15 = 0
D) x² - 2x - 15 = 0

3 Answers

what is DK? (Dinesh Kartik? the idiot who stopped sachin's 100 and almost prevented gambhir from his 150?)

106

Asish Mahapatra ·2009-12-27 23:26:11

1/a_r+1 - 1/a_r = d
=> a_r - a_r+1d = a_ra_r+1
where d is the CD of the AP

so summing this from r=1 to 3,

we get (a₁-a₄)/a₁a₄d

now 1/a₄ = 1/a₁ + 3d

so the exp is 3

now 3 is a root of (B)

nishant sir pls see ur chatbox

YUP Asish ... Right.

@Nishant Sir .... DK's not that idiot. DK means Dark Knight.....

though Nishant Bhaiya doesn't watch Eng Movies too often ....lolzzzz Dinesh Kartik HO HO :- D

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