If the m^th term of an AP is 1/n and n^th term of an ap is 1/m than prove that Smn=1/2(mn+1)

If the m^th term of an AP is 1/n and n^th term of an ap is 1/m than pr

1.	If the m^th term of an AP is 1/n and n^th term of an ap is 1/m than prove that Smn=1/2(mn+1)
Answer» According to the questionA+(m-1)d=1/n-------(1)A+(n-1)d=1/m-------(2)(1)-(2)(m-1)d-(n-1)d=1/n-1/mTaking d common in LHS and taking LCM in RHSd(m-1-n+1)=(m-n)/mnd(m-n)=(m-n)/mnd=1/mn--------------(3)Using (3) in (1)A+(m-1)/mn=1/nA+1/n-1/mn=1/nA=1/mn-------------(4)Sum of mn terms=mn(2A+(mn-1)d)/2=mn(2/mn+(mn-1)/mn)/2=mn(2/mn+1-1/mn)/2=mn(1/mn+1)/2=mn(1+mn/2mn)=(1+mn)/2