The sum of the infinite series 1 + 2 3 + 7 3 2 + 12 3 3 + 17 3 4 + 22 3 5 + … … is equal to:

Question

The sum of the infinite series 1 + 2 3 + 7 3 2 + 12 3 3 + 17 3 4 + 22 3 5 + … … is equal to:, 9 4, 15 4, 11 4, 13 4

MARKS App · Accepted Answer

S = 1 + 2 3 + 7 3 2 + 12 3 3 + 17 3 4 + … S 3 = 1 3 + 2 3 2 + 7 3 3 + 12 3 4 + … 2 S 3 = 1 + 1 3 + 5 3 2 + 5 3 3 + 5 3 4 + … + up to infinite terms ⇒ 2 S 3 = 4 3 + 5 9 1 1 - 1 3 ⇒ 2 S 3 = 13 6 ⇒ S = 13 4

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