If a 1- a 2- a n be in AP of non zero terms then prove that 1 -a1 a2-1 -a2 a3- - -1 -an-1 an-n-1 -a1 an

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Property 2

If a 1, a 2… ...

Question

If a₁,a₂.....a_n be in AP of non zero terms then prove that
1/(a₁a₂) + 1/(a₂a₃)+........+1/(a_n-1a_n) = (n-1) /(a₁a_n)

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If $a_{1}, a_{2}, a_{3}, . . . ., a_{n}$ be an AP of non-zero terms. Prove that

$\frac{1}{a_{1} a_{2}}$ + $\frac{1}{a_{2} a_{3}}$ +....+ $\frac{1}{a_{n - 1} a_{n}}$ =

$\frac{n - 1}{a_{1} a_{n}}$

If $a_{1}, a_{2}, a_{3}, \dots, a_{n}$ be an AP of nonzero terms then prove that

$\frac{1}{a_{1} a_{2}} + \frac{1}{a_{2} a_{3}} + \frac{1}{a_{3} a_{4}} + \dots + \frac{1}{a_{n - 1} a_{n}} = \frac{(n - 1)}{a_{1} a_{n}}$

a_{1}, a_{2}, a_{3}, . . . . . . a_{n}

\frac{1}{a_{1} a_{2}} + \frac{1}{a_{2} a_{3}} + . . . . . + \frac{1}{a_{n - 1} a_{n}} =

\frac{1}{a_{1} a_{2}} + \frac{1}{a_{2} a_{3}} + . . . + \frac{1}{a_{n - 1} a_{n}} = \frac{n - 1}{a_{1} a_{n}} .

a_{1}, a_{2}, a_{3}, . . . .,

\frac{1}{a_{1} a_{2}} + \frac{1}{a_{2} a_{3}} + \frac{1}{a_{3} a_{4}} + . . . . . + \frac{1}{a_{n - 1} a_{n}}

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