Question

The nth term of the series 1/(4.7)+1/(7.10)+1/(10.13)+.....is how to solve it?​

Answer 1

Given:

1/(4.7)+1/(7.10)+1/(10.13)+.....

To find:

The nth term of the series.

Solution:

1) To find the nth term of the given series we will first find the series for the given options.

      a) (1/3)[1/(3n+1) - 1/(3n+4)]

                   now put the value of n as 1, 2, 3, and so on,

• (1/3)[1/(3.1+1) - 1/(3.1+4)] + (1/3)[1/(3.2+1) - 1/(3.2+4)] + (1/3)[1/(3.3+1) - 1/(3.3+4)] .....

• (1/3)[1/4-1/7] + (1/3)[1/7-1/10] + (1/3)[1/10-1/13].....

• (1/3)[7-4/4.7] + (1/3)[10-7/7.10] + (1/3)[13-10/10.13].......

• (1/3)[3/4.7] + (1/3)[3/7.10] + (1/3)[3/10.13]............

• 1/(4.7)+1/(7.10)+1/(10.13)...........

We get the required series in the first option only so no need to check further.

The nth term of the given series is (1/3)[1/(3n+1) - 1/(3n+4)].