Consider the sequence 1, 2, 1, 2, 2, 1,2, 2,2, 1, 2, 2, 2,2, 1..... The sum of the digit in 'n' such that the first'n' terms sum up to 2010.

Consider the sequence a _(n+1) = (1)/( 1 - a _(n)) , nge 1 Given that a _(1) = (1)/(2) find sum of first 100 terms of this sequence

If the sum of the first n terms of a sequence is equal to √ (3/ 2) ( n^ 2 − n ) , then the sum of the squares of these terms is equal to

Find the n^(th) term of the sequence 1/n^2, (1+n^2)/n^2, (1+2n^2)/n^2,...

if the sum of m terms of an A.P is to the sum of n terms as m^(2) to n^(2) show that the mth term is to the n th term as 2m-1 to 2n-1

The sum of first n terms of the sequence 1,1+2,(1+2+2^(2)),....,(1+2+2^(2)+.....+2^(k)-1) , is of the form 2^ (n + R) + S n^ 2 + T n + U , t h e n The value of ( R + S + T + U ) is-

The sum of the digits in (10^(2n^(2)+5n+1)+1)^(2) (where n is a positive integer),is

The sum of first n terms of an arithmetic sequence is n^2+2n Prove that the sum of continuous terms starting from the first of the sequence 3,5,7,..... added to 1 gives a perfect square.

Find the sum of first n terms of the following 1+(1+2)+(1+2+3)+….

Find the sum of first n term of the following series 1+(1+2)+(1+2+2^2)+ …..