Find the sum to n terms of the series 1/(1 x 2), 1/(2 x 3), 1/(3 x 4) +...

Solution:

The given series is 1/(1 x 2), 1/(2 x 3), 1/(3 x 4) + .... n terms.

Hence,

a_n = 1/n (n + 1)

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

Therefore,

a₁ = 1/1 - 1/2

a₂ = 1/2 - 1/3

a₃ = 1/3 - 1/4

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

Adding the above terms column wise, we obtain

a₁ + a₂ + .... n = [1/1 + 1/2 + 1/3 + .... + 1/n] - [1/1 + 1/2 + 1/3 + .... + 1/(n + 1)]

Thus,

S_n = 1 - 1/(n + 1)

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

= n/(n + 1)

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NCERT Solutions Class 11 Maths Chapter 9 Exercise 9.4 Question 4

Find the sum to n terms of the series 1/(1 x 2), 1/(2 x 3), 1/(3 x 4) + ....

Summary:

We know that a_n = 1/n (n + 1) therefore by finding out a couple of initial elements and adding them the sum comes out to be n/(n + 1)