`(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)))

Statement -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)) Statement -2: (1)/(1.3)+(1)/(3.5)+(1)/(5.7)+ . . . .+(1)/((2n-1)(2n+1))=(1)/(2n+1)

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

Find the sum (1^(4))/(1xx3)+(2^(4))/(3xx5)+(3^(4))/(5xx7)+......+(n^(4))/((2n-1)(2n+1))

1.4+2.5+.......+n(n+3)=

Using the principle of mathematical induction prove that (1)/(1.2.3)+(1)/(2.3.4)+(1)/(3.4.5)+...+(1)/(n(n+1)(n+2))=(n(n+3))/(4(n+1)(n+2) for all n in N

Prove the following by using the principle of mathematical induction for all n in Nvdots(1)/(1.2.3)+(1)/(2.3.4)+(1)/(3.4.5)+...+(1)/(n(n+1)(n+2))=(n(n+3))/(4(n+1)(n+2))

Prove the following by using the principle of mathematical induction for all n in Nvdots(1)/(2.5)+(1)/(5.8)+(1)/(8.11)+...+(1)/((3n-1)(3n+2))=(n)/((6n+4))=(n)/((6n+4))

1^(3)+2^(3)+3^(3)+.....+n^(3)=(n(n+1)^(2))/(4), n in N

1.2.3+2.3.4++n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/(4)