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(1)/(1.3)+(1)/(3.5)+(1)/(5.7)+.....+(1)/...

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

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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)

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)

underset(n to oo)lim {(1)/(1.3)+(1)/(3.5)+(1)/(5.7)+.....+(1)/((2n-1)(2n+1))}=

lim_(n rarr oo){(1)/(1.3)+(1)/(3.5)+(1)/(5.7)+....+(1)/((2n+1)(2n+3 ))

Prove by the method of induction, (1)/( 1.3) + (1)/( 3.5) + (1)/( 5.7) + . . . + (1)/( (2n - 1)(2n + 1)) = (n)/(2 n +1)

Prove that by using the principle of mathematical induction for all n in N : (1)/(3.5)+ (1)/(5.7)+ (1)/(7.9)+ ....+(1)/((2n+1)(2n+3))= (n)/(3(2n+3))

Prove that by using the principle of mathematical induction for all n in N : (1)/(3.5)+ (1)/(5.7)+ (1)/(7.9)+ ....+(1)/((2n+1)(2n+3))= (n)/(3(2n+3))

Prove that by using the principle of mathematical induction for all n in N : (1)/(3.5)+ (1)/(5.7)+ (1)/(7.9)+ ....+(1)/((2n+1)(2n+3))= (n)/(3(2n+3))

Prove the following by using the principle of mathematical induction for all n in Nvdots(1)/(3.5)+(1)/(5.7)+(1)/(7.9)+...+(1)/((2n+1)(2n+3))=(n)/(3(2n+3))

lim_(n rarr oo)((1)/(1.3)+(1)/(3.5)+.............+(1)/((2n-1)(2n+) 1)))