If `a_(n) = (n^(2))/(2^(n))`, then find `a_(7)`.

If a_(n)=(n(n-2))/(n+3) : find the term a_(20^(@))

If a_n =(2n-3)/6 , then find a_(10) ?

If n^(th) term of the sequences is a_(n)= (-1)^(n-1)5^(n+1) , Find a_(3) ?

If (1 +x + x^(2))^(n) = a_(0) + a_(1) x + a_(2) x^(2) + … + a_(2n) x^(2n) , then a_(0) + a_(2) + a_(4) + … + a_(2n) equals

Let a_(n)=(1000^(n))/(n!) for n in N . Then a_(n) is greatest when:

The nth term of a series is given by t_(n)=(n^(5)+n^(3))/(n^(4)+n^(2)+1) and if sum of its n terms can be expressed as S_(n)=a_(n)^(2)+a+(1)/(b_(n)^(2)+b) where a_(n) and b_(n) are the nth terms of some arithmetic progressions and a, b are some constants, prove that (b_(n))/(a_(n)) is a costant.

If (1+x+x^(2))^(n) = sum_(r=0)^(2 n) a_(r). x^(r) then a_(1)-2 a_(2)+3 a_(3)-..-2 n. a_(2n) =

The sequence a_(1),a_(2),a_(3),".......," is a geometric sequence with common ratio r . The sequence b_(1),b_(2),b_(3),".......," is also a geometric sequence. If b_(1)=1,b_(2)=root4(7)-root4(28)+1,a_(1)=root4(28)" and "sum_(n=1)^(oo)(1)/(a_(n))=sum_(n=1)^(oo)(b_(n)) , then the value of (1+r^(2)+r^(4)) is

If f:NtoR, where f(n)=a_(n)=(n)/((2n+1)^(2)) write the sequence in ordered pair from.