If the mth term of an AP IS 1÷n and nth term is 1÷m ,then show that the sum of mn term is 1÷2 (mn+1).
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SakshaM725:
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Therefore, Am = a+ (m-1)d=1/n ….(i)
An = a+(n-1)d=1/m ….(ii)
Subtracting equation (ii) from (i)
d[(m-1)-(n-1)] = 1/n-1/m,
d(m-n) = (m-n)/mn,
d = 1/mn ….(iii)
Substituting equation (iii) in (i)
a+(m-1)/mn = 1/n,
a = 1/n[1-(m-1)/m],
a = 1/mn ….(iv)
Now Amn i.e the mnth term of AP = a+(mn-1)d,
Step-by-step explanation:
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