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n
th term of the sequence {an} is such that
a1 = 1/2, (n - 1) an+1 = (n + 1)an + 1(n ≥ 2).
Find a2
For any positive integer n define E(n) = n(n + 1)(2n + 1)(3n + 1).....(10n + 1)
Find the sum of digits of the greatest common divisor of E(1), E(2), E(3),.....Ε(2009)
2025 japan tst p1
HInt: prove the seqn is bounded
assume the bound to be k then assume a_2025\neq k and get contra and prove all terms are equal
