Find the sum of series of form `1/(a(a+d))+1/((a+d)(a+2d))+1/((a+2d)(a+3d))+..........1/((a+(n-2)d)(a+(n-1)d))`

lim_(x rarr oo){(1)/(a(a+d))+(1)/((a+d)(a+2d))+(1)/((a+2d)(a+3d))+............ nterms

a+(a+d)+(a+2d)+....+[a+(n-1)d]=(n)/(2)(2a+(n-1)d)

let a>0,d>0 find the value of the determinant (1)/(a)_((1)/(a(a+d))),(1)/((a+d)(a+2d))(1)/(a+d),(1)/((a+d)(a+2d)),(1)/((a+2d)(a+3d))(1)/(a+2d),(1)/((a+2d)(a+3d)),(1)/((a+3d)(a+4d))]|

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

The sum of the series 1/(1!(n-1)!)+1/(3!(n-3)!)+1/(5!(n-5)!)+…..+1/((n-1)!1!) is = (A) 1/(n!2^n) (B) 2^n/n! (C) 2^(n-1)/n! (D) 1/(n!2^(n-1)

The sum of the series a-(a+d)+(a+2d)-(a+3d)+... up to (2n+1) terms is -nd b.a+2nd c.a+ndd .2nd

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

If C_(r) stands for nC_(r), then the sum of first (n+1) terms of the series aC_(0)-(a+d)C_(1)+(a+2d)C_(2)-(a+3d)C_(3)+...... is