Question

if 1/1x2 + 1/2x3 + 1/3x4 ... + 1/{nx(n+1)} = 19/20, then n is

Answer 1

Step-by-step explanation:-

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1/(1*2) + 1/(2*3) + 1/(3*4) + ... + 1/(n*(n+1)) = n/(n+1)

By Induction

1. We check it for n=1. If n=1, then we have  

1/(1*2)=1/2, which is true

Now assume this is true for n=k and show that it is true for n=k+1 as well

 

1/(1*2) + 1/(2*3) + 1/(3*4) + ... + 1/(k*(k+1))+1/((k+1)*(k+2)) =

=k/(k+1)+1/((k+1)(k+2))=(k+1)/(k+2)

 

Note: You can prove it without induction as well:

1/(1*2) + 1/(2*3) + 1/(3*4) + ... + 1/(n*(n+1)) =

=(1/1-1/2)+(1/2-1/3)+...(1n-1/(n+1))=1-1/(n+1)=n/(n+1)

Answer 2

Step-by-step explanation:

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