If A r = 1 r r + 1 1 3 r 2 3 , then lim n → ∞ ⁡ ∑ r = 1 n A r is equal to

Question

If A r = 1 r r + 1 1 3 r 2 3 , then lim n → ∞ ⁡ ∑ r = 1 n A r is equal to, 0, 2, 4, 8

MARKS App · Accepted Answer

A r = 1 r r + 1 1 3 r 2 3 = 1 r - 1 r + 1 1 3 r 2 3 ⇒ lim n → ∞ ⁡ ∑ r = 1 n A r = 1 - 1 2 + 1 2 - 1 3 + 1 3 - 1 4 + … 1 3 + 1 3 2 + 1 3 3 + … 2 3 = 1 1 3 1 - 1 3 2 3 = 1 1 2 2 3 = 3 - 1 = 2

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