Find the sum of n terms and sum to infinity of the following series : `(1)/(2cdot4)+(1)/(4cdot6)+(1)/(6cdot8)+…`

Find the nth term sum of n terms and sum to infinity terms of the series (1)/(2.5)+(1)/(5.8)+ (1)/(8.11)+ ...

The sum to infinity of the series (1)/(2.4)+(1)/(4.6)+(1)/(6.8)+(1)/(8.10)+...... is

If the sum to infinity of the series 3+(3+d) (1)/(4) +(3+2d) (1)/(4^(2))+cdots oo is (44)/(9) then find d.

Find the nth terms and the sum to n term of the series : 1.4.7+2.5.8+3.6.9 + ...

If S denotes the sum to infinity and S_(n) , denotes the sum of n terms of the series 1+(1)/(2)+(1)/(4) + (1)/(8)+ cdots , such that S-S_(n) lt (1)/(100) , then the least value of n is

Sum the series to infinity : 1 +(1)/(2) +(1)/(4) +(1)/(8) + ...

Let A, be the sum of the first n terms of the geometric series 704 + (704)/(2) +(704)/(4) +(704)/(8)+ cdots and B_(n) , be the sum of the first n terms of the geometric series 1984 - (1984)/(2) + (1984)/(4) -(1984)/(8) + cdots If A_(n), =B_(n) , then the value of n is (where n in N).

Find the nth term and the sum of n terms of the series 1.2.4+2.3.5+3.4.6+....