Question

if mth term of an ap is 1/n and nth term is 1/m, then find the sum of its first m n terms​

Answer 1

Answer:

Let the first term and common difference of AP be a and d respectively.

Given: mth term= 1/n

=> a+(m-1)d =1/n ……(A)

And, nth term=1/m

=> a+(n-1)d=1/m …….(B)

(A) - (B) gives

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

=> d = 1/mn ……(C)

Now, using (A) putting the value of d ,we get

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

=> a + 1/m - 1/mn =1/n

=> a=1/n - 1/m + 1/mn ……(D)

mn th term = a+(mn-1)d = 1/n - 1/m + 1/mn +(mn-1)/mn { Using (C) and (D)

=1/n - 1/m + 1/mn + 1 - 1/mn = 1/n - 1/m + 1

Answer 2

here is your answer