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If mth term of an AP is 1/n and its nth ...

If mth term of an AP is 1/n and its nth term is 1/m , then show that its (mn)th term is 1

Text Solution

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`a_m=a+(m-1)d=1/n-(1)`
`a_n=a+(n-1)d=1/n-(2)`
subtracting equation 1 from from equation 2
`(n-1)d-(m-1)d=1/m-1/n`
`d(n-1-m+1)=(n-m)/(nm)`
`d=1/(nm)`
`a=1/n-(m-1)/(nm)`
`a=(m-m+1)/(nm)`
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