Question

If the mth term of an ap is 1/n and nth term is 1/m then find the sum of its first mn terms

Answer 1

Step by step explanation

Answer 2

Answer:

Step-by-step explanation:

Given :-

mth term of an ap is 1/n and nth term is 1/m.

To Find :-

The sum of first mn terms.

Solution :-

Let the 1st term is a and common difference is d of the given A.P.

According to the Question,

Therefore, a(m) = a + (m - 1)d = 1/n ..... (i)

And, a(n) = a + (n - 1)d = 1/m ..... (ii)

On Subtracting Eq (ii) from (i), we get

(m - 1)d = 1/n - 1/m = m - n/mn

or, d = 1/mn

and, a = 1/mn

Now, S(mn) = mn/2[2 × 1/mn + (mn - 1)1/mn]

= mn/2[2/mn + mn/mn - 1/mn]

S(mn) = mn/2[1/mn + 1]

= 1/2[mn + 1]

Hence, the sum of first mn terms is 1/2[mn + 1]