If b is the first term of an infinite geometric progression whose sum is five, then b lies in the interval

Question

If b is the first term of an infinite geometric progression whose sum is five, then b lies in the interval, 10 , ∞, - ∞ , - 10, - 10 , 0, 0 , 10

MARKS App · Accepted Answer

If b is the first term and r is the common ratio of an infinite G.P. and sum is 5 , then 5 = b 1 - r ⇒ 1 - r = b 5 ⇒ r = 1 - b 5 ⇒ r = 5 - b 5 ∴ - 1 r 1 ∴ - 1 5 - b 5 1 ⇒ - 5 5 - b 5 ⇒ - 10 - b 0 ⇒ 0 b 10 ⇒ b ∈ 0 , 10

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