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

Explanation

Let `S(n)=1/(2.5)+1/(5.8)​+1/(8.11)​+.........+1/((3n−1)(3n−2))`

Step - (1)

prove `s(n)` for `n=1`

`L.H.S=1/(2.5)+1/(5.8)​+1/(8.11)​+.......+1/((3(1)−1)(3(1)+2))​`

`=1/(2.5)​+1/(5.8)​+1/(8.11)​+........+1/(2.5)`

L.H.S`=1/(2.5)​=1/(10)`
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R.H.S`=1/(2.5)​=1/(10)`​

So, it is true for `n=1`

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