The sequence is 36,34,32,30,3−2,… so an=38−2n.
Pn=k=1∏n38−2k=3∑k=1n(8−2k)=38n−n(n+1)=3n(7−n)
(Pn)1/n=37−n
2n=1∑4037−n=2(36+35+⋯+3−33)=2⋅36⋅1−1/31−3−40=37−3−33
=333340−1
So α=40,β=33.
Since gcd(40,33)=1, we get α+β=73.
JEE Main 2026 — Mathematics Algebra
Let 729,81,9,1,… be a sequence and Pn denote the product of the first n terms of this sequence.
If 2n=1∑40(Pn)n1=3β3α−1 and gcd(α,β)=1,
then α+β is equal to
Held on 24 Jan 2026 · Verified 6 Jul 2026.
74
76
73
75
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