Let 729,81,9,1, . . . be a sequence and P _n denote the product of the first n terms of this sequence. If 2 \sum_{n=1}^{40} ( P _n) ^{\frac{1}{n}}=\frac{3^\alpha-1}{3^\beta} and {\gcd}(\alpha, \beta)=1, then \alpha+\beta is equal to [24 jan 2026 Shift 1]

Sequences and Series Part 3

Section: Mathematics

Question : 9 of 93

Marks: +1, -0

Let 729,81,9,1,... be a sequence and Pn denote the product of the first n terms of this sequence.
If 2‌

∑

n=1

(Pn)‌

=‌

3α−1

3β

and gcd(α,β)=1, then α+β is equal to

[24 jan 2026 Shift 1]

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