Question

the nth term of the sequence 1/2,1/6,1/12,....is

Answer 1

Given : sequence 1/2 , 1/6 , 1/12

To Find :  nth term of the sequence

Solution:

1/2 , 1/6 , 1/12

1/2  = 1/(1. 2)    - 1st Term

1/6  = 1/(2.3)  - 2nd term

1/12  = 1/(3.4)  - 3rd term

Hence nth term will be

1/(n.(n+1)

nth term of the sequence 1/2 , 1/6 , 1/12   .....  is 1/(n.(n+1)

1/(n.(n+1)  = 1/n - 1/(n+1)

Additional info :

1 - 1/2  + 1/2 - 1/3 + 1/3 - 1/4  +.........................................+ 1/n - 1/(n+1)

=   1 - 1/(n+1)

=(n + 1 - 1)/(n + 1)

= n/(n+1)

Sum of sequence of terms would be  1 - 1/(n+1)  =  n/(n+1)

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Answer 2

Answer:

1/n^2 +n............