যদি `n_(1), n_(2) "এবং" n_(3)` হল তিনটি সেগমেন্টের মৌলিক ফ্রিকোয়েন্সি যার মধ্যে রয়েছে

If S_(1),S_(2)andS_(3) denote the sum of first n_(1)n_(2)andn_(3) terms respectively of an A.P., then (S_(1))/(n_(1))(n_(2)-n_(3))+(S_(2))/(n_(2))+(n_(3)-n_(1))+(S_(3))/(n_(3))(n_(1)-n_(2)) =

If n_(1) , n_(2) , n_(3) ,….., n_(100) are positive real numbers such that n_(1)+n_(2)+n_(3)+…+n_(100)=20 and k=n_(1)(n_(2)+n_(3)+n_(4))(n_(5)+n_(6)+…+n_(9))(n_(10)+….+n_(16))…(…+n_(100)) , then k belongs to

Show that ((n+1)!)/((n-2)!)=n^(3)-n3

If P(n) :1+4+7…….+(3n-2)=(1)/(2)n(3n-1) .Verify P(n) for n =1,2.

For two Bohr orbits n_(1) "and"n_(2) which follow the relationships, (n_(2)^(2)=n_(1)^(2))=21 and (n_(2) - n_(1))=3. If an electron makes transition from n_(2) "to" n_(1) directly then :

If n_(1)+n_(2)+n_(3)+n_(4)=20 such that n_(i)gei+1AAiepsilon{1,2,3,4} and n_(i)"" epsilonI then number of solutions are

Prove that ((2n)!)/(2^(2n)(n!)^(2))<=(1)/(sqrt(3n+1)) for all n in N