Question

For an increasing G.P. a₁, a₂ , a₃ ........., a_n, if a₆ = 4a₄, a₉ – a₇ = 192, then the value of `sum_(i = 1)^∞ 1/a_i` is ______.

पर्याय

• 0.00

• 1.00

• 2.00

• 3.00

Answer 1

For an increasing G.P. a₁, a₂ , a₃ ........., a_n, if a₆ = 4a₄, a₉ – a₇ = 192, then the value of `sum_(i = 1)^∞ 1/a_i` is 2.00.

Explanation:

a₆ = 4a₄

⇒ ar⁵ = 4ar³

⇒ r² = 4

⇒ r = ±2

But for increasing,

r = 2

a₉ – a₇ = 192

⇒ ar⁸ = ar⁶  = 192

ar⁶(r² – 1) = 192

a2⁶(3) = 192

⇒ a = 1

`sum_(i = 1)^∞ 1/a_i = 1/1 + 1/2 + 1/4 + ...... + ∞`

= `1/((1 - 1/2))`

= 2