If a1, a2, a3, ⋯, an be an AP of nonzero terms then prove that 1a1a2

1.	If a1, a2, a3, ⋯, an be an AP of nonzero terms then prove that 1a1a2+1a2a3+1a3a4+⋯+1an−1an=(n−1)a1an
Answer» If $a_{1}, a_{2}, a_{3}, \dots, a_{n}$ be an AP of nonzero terms then prove that $\frac{1}{a_{1} a_{2}} + \frac{1}{a_{2} a_{3}} + \frac{1}{a_{3} a_{4}} + \dots + \frac{1}{a_{n - 1} a_{n}} = \frac{(n - 1)}{a_{1} a_{n}}$

If a1, a2, a3, ⋯, an be an AP of nonzero terms then prove that 1a1a2+1a2a3+1a3a4+⋯+1an−1an=(n−1)a1an

Answer»

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

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