aaaaa.....AP...

if a1,a2,........,an+1 arev in ap,then
1a1a2+1a2a3+......1anan+1 is.....??????

2 Answers

206
Sayantan Hazra ·

try to change 1a1a2 in the form of k(1a1 - 1a2) and then solve.....

206
Sayantan Hazra ·

1a1a2 = k(1a1 - 1a2)

→ 1 = k(a2 - a1)
→ 1 = kd, d: common difference
→ k = 1d

Hence, we can write all the terms as:
1a1a2 = 1d(1a1 - 1a2) ...................(1)
1a2a3 = 1d(1a2 - 1a3) ......................(2)

and so on, till

1an-1an = 1d(1an-1 - 1an)....................(n)

Now add all these to get the required sum

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