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The sum to infinity of a geometric progression is 39/2. The sum to infinity to squares of the terms of the geometric progression is 253.5. What is the sum to infinity of cubes of the terms of the geometric progression?

The sum to infinity of a geometric progression is 39/2. The sum to infinity to squares of the terms of the geometric progression is 253.5. What is the sum to infinity of cubes of the terms of the geometric progression? Correct Answer 3827.03

Given:

The sum to infinity of a geometric progression is 39/2

Calculation:

Let the first term and common ratio of the geometric progression be a and r respectively

⇒ (a/1 - r) = 39/2       ------(1)

⇒ (a2/1 - r2) = 253.5 = 507/2      ------(2)

⇒ (a/1 - r)2 = (39/2)2       ------(3)     (squaring (1) on both sides)

⇒ Dividing (2) by (3) and simplifying

⇒ r = 1/5, a = (39/2) × (1 - r) = 78/5

⇒ Sum of the cubes of the terms of the geometric progression

⇒ a3/(1 - r3) = (78 × 78 × 78)/124 = 3827.03     which is > 1000

∴ The required result will be 3827.03.

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