Home
Class 12
MATHS
1^2/(1.3)+2^2/(3.5)+3^2/(5.7)+.....+n^2/...

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

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBER

    FIITJEE|Exercise SOLVED PROBLEMS (SUBJECTIVE)|20 Videos

  • COMPLEX NUMBER

    FIITJEE|Exercise SOLVED PROBLEMS (OBJECTIVE)|30 Videos

  • CIRCLE

    FIITJEE|Exercise Numerical Based|2 Videos

  • DEFINITE INTEGRAL

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

Similar Questions

Explore conceptually related problems

(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))

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

((2n+1)!)/((2n-1)!)*((n-1)!)/((n+2)!)=(3)/(5)

Using the principle of mathmatical induction, prove each of the following for all n in N 1/(1*3)+1/(3*5)+1/(5*7)+...+1/((2n-1)(2n+1))=n/((2n+1))

Prove the following by the principle of mathematical induction: (1)/(3.5)+(1)/(5.7)+(1)/(7.9)+(1)/((2n+1)(2n+3))=(n)/(3(2n+3))

(1^(3)+2^(3)+...+n^(3))/(1+3+5+...+(2n-1))=((n+1)^( 2))/(4)

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