a_(n)=(2n-3)/(6)

A sequence of numbers A_(n)n=1,2,3... is defined as follows: A_(1)=(1)/(2) and for each n>=2,A_(n)=((2n-3)/(2n))A_(n-1), then prove that sum_(k=1)^(n)A_(k) =1

Find the indicated terms in each of the following sequences whose nth terms are: a_(n)=5_(n)-4;a_(12) and a_(15)a_(n)=(3n-2)/(4n+5);a+7 and a_(8)a_(n)=n(n-1);a_(5)anda_(8)a_(n)=(n-1)(2-n)3+n);a_(1),a_(2),a_(3)a_(n)=(-1)^(n)n;a_(3),a_(5),a_(8)

Find a_(1),a_(2),a_(3) if the n^(th) term is given by a_(n)=(n-1)(n-2)(3+n)

If (1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+a_(3)x^(3)+.....+a_(2n)x^(2n)" prove that",a_(0)+a_(2)+a_(4)+.......a_(2n)=(1)/(2)(3^(n)+1) .

If a_(n) = (n(n+3))/(n+2) , then find a_(17) .

If a_(1),a_(2),a_(3),......,a_(n) are consecutive terms of an increasing A.P.and (1^(2)-a_(1))+(2^(2)a_(2))+(3^(2)a_(3))+.........+(n^(2)-a_(n))=((n-1)*n*(n+1))/(3) then the value of ((a_(5)+a_(3)-a_(2))/(6)) is equal to

If (1^(2)-a_(1))+(2^(2)-a_(2))+(3^(2)-a_(3))+…..+(n^(2)-a_(n))=(1)/(3)n(n^(2)-1) , then the value of a_(7) is

If (1^(2)-a_(1))+(2^(2)-a_(2))+(3^(2)-a_(3))+…..+(n^(2)-a_(n))=(1)/(3)n(n^(2)-1) , then the value of a_(7) is

Find the term indicated in each case: (i) a_(n)=(n^(2))/(2^(n)):a_(7) (ii) a_(n)=(n(n-2))/(n-3),a_(20) (iii) a_(n)=[(1+(-1)^(n))/2 3^(n)],a_(7)