Question

If the mth term of an A.P. is 1/n and nth term is 1/m , then show that the sum of the m and n terms is 1/2(mn+1).

Answer 1

a(m) = a + (m-1)d = 1/n

a(n) = a + (n-1)d = 1/m

subtracting both equations, we get

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

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

= d = 1/mn

Putting d = 1/mn , we get

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

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

= a = 1/mn

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

= (mn+1)/2

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