Home
Class 11
MATHS
Prove the following by using the princip...

Prove the following by using the principle of mathematical induction for all `n in N`:`1/(2. 5)+1/(5. 8)+1/(8. 11)+...+1/((3n-1)(3n+2))=n/((6n+4))`

Text Solution

AI Generated Solution

To prove the statement \[ \frac{1}{(2 \cdot 5)} + \frac{1}{(5 \cdot 8)} + \frac{1}{(8 \cdot 11)} + \ldots + \frac{1}{((3n-1)(3n+2))} = \frac{n}{(6n+4)} \] for all \( n \in \mathbb{N} \) using the principle of mathematical induction, we will follow these steps: ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    NCERT|Exercise EXERCISE 4.1|24 Videos

  • PERMUTATIONS AND COMBINATIONS

    NCERT|Exercise EXERCISE 7.2|5 Videos

  • PROBABILITY

    NCERT|Exercise EXERCISE 16.3|21 Videos

Similar Questions

Explore conceptually related problems

Prove the following by using the Principle of mathematical induction AA n in N 2^(n+1)>2n+1

Prove the following by using the principle of mathematical induction for all n in Nvdots(2n+7)<(n+3)^(2)

Prove the following by using the principle of mathematical induction for all n in Nvdots(1)/(1.4)+(1)/(4.7)+(1)/(7.10)+...+(1)/((3n-1)(3n+1))=(n)/((3n+1))

Prove the following by using the principle of mathematical induction for all n in Nvdots1+2+3+...+n<(1)/(8)(2n+1)^(2)

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))

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 Nvdots10^(2n-1)+1 is divisible by 11.

Prove the following by the principle of mathematical induction: 1+2+2^(7)=2^(n+1)-1 for all n in N

Prove the following by using the principle of mathematical induction for all n in Nvdots(1)/(2)+(1)/(4)+(1)/(8)+...+(1)/(2^(n))=1-(1)/(2^(n))

Prove the following by using the principle of mathematical induction for all n in Nvdotsn(n+1)(n+5) is a multiple of 3.

Home
Profile