If mth term of an A.p. is 1/n and nth term is 1/m , show the sum of its first (mn) term is 1/2(mn+1)

If mth term of an A.p. is 1/n and nth term is 1/m , show the sum of it

1.	If mth term of an A.p. is 1/n and nth term is 1/m , show the sum of its first (mn) term is 1/2(mn+1)
Answer» By solving am=1/n we get equation i.e.,a+dm-d=1/n. Similarly solving an=1/m we get equation i.e.,a+dn-d=1/m. By eliminating these two equations we d=1/mn. Substitute this value of d in equation 1 . We get a=1/mn. Then find Amn,we Amn=1. By this find Smn i.e., Smn=mn/2{a+Amn} we get 1/2{mn+1]. Hence proved.... I/n=a+(m-1)d......1/m=a+(n-1)d.........subtract......1/n-1/m=a-a+(m-1-n+1)d..........(m-n)/mn=(m-n)d.......d=1/mn......put the value of d in eq (1) you get a=1/mn.......now put the formulae of sn.......mn/2[(2/mn+(mn-1)1/mn]........mn/2(2+mn-1)1/mn....then we get sn=1/2(mn+1) Question galat h aapka