(1)/(2.5)+(1)/(5.8)+(1)/(8.11)+...+(1)/((3n-1)(3n+2))=(n)/((6n+4))

(1)/(2.5)+(1)/(5.8)+(1)/(8.11)+... n terms =(A)(n)/(6n+4) (B) (n)/(3n+2)(C)(n)/(4n+6)(D)(1)/(2(2n+3))

(1^(2))/(1.3)+(2^(2))/(3.5)+(3^(2))/(5.7)+.....+(n^(2))/ ((2n-1)(2n+1))=((n)(n+1))/((2(2n+1)))

(1^(4))/(1.3)+(2^(4))/(3.5)+(3^(4))/(5.7)+......+(n^(4)) /((2n-1)(2n+1))=(n(4n^(2)+6n+5))/(48)+(n)/(16(2n+1))

1^2/(1.3)+2^2/(3.5)+3^2/(5.7)+.....+n^2/((2n-1)(2n+1))=((n)(n+1))/((2(2n+1))

Prove that 1^2/(1.3)+2^2/(3.5)+3^2/(5.7)+.....+n^2/((2n-1)(2n+1))=((n)(n+1))/((2(2n+1))

1^2/(1.3)+2^2/(3.5)+3^2/(5.7)+.....+n^2/((2n-1)(2n+1))=((n)(n+1))/((2(2n+1))

Prove that (C_1)/(2) + (C_3)/(4) + (C_5)/(6) + (C_7)/(8) + …… = (2^n - 1)/(n+ 1)

lim_(n rarr oo)((n^(3)-2n^(2)+1)^((1)/(2))+(n^(4)+1)^((1)/(3 ))))/((n^(6)+6n^(5)+2)^((1)/(4))-(n^(7)+3n^(2)+1)^((1 )/(5)))

The sum of the series 1+4+3+6+5+8+ upto n term when n is an even number (n^(2)+n)/(4) 2.(n^(2)+3n)/(2) 3.(n^(2)+1)/(4) 4.(n(n-1))/(4)(n^(2)+3n)/(4)