The sum to infinity of 1 + 2/3 + 3/9 + 4/27 + ... (nth term n/3 n−1 ) is:

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The sum to infinity of 1 + 2/3 + 3/9 + 4/27 + ... (nth term n/3<sup>n−1</sup>) is:

Answer: 9/4.

Correct answer: B. 9/4

Explanation: This is Σ n·x<sup>n−1</sup> with x = 1/3, which equals 1/(1−x)² = 1/(2/3)² = 9/4.

Bar heights for AP 2, 5, 8, 11 with the common difference d=3 marked between consecutive terms.

Arithmetic progressions, geometric progressions, and sums