If the mth term of an A.P. be `1//n` and nth term be `1//m` then show that its (`m n` ) term is 1.

Answer

N/a

Explanation

Let first term and common difference of A.P. be 'a' and 'd' respectively.
`T_(m)=(1)/(n)`
`rArr " "a+(m-1)d=(1)/(n)" "...(1)`
`T_(n)=(1)/(m)`
`rArr " "a+(n-1)d=(1)/(m)" "...(2)`
Subtract eq. (2) from eq. (1)
`(m-n)d=(1)/(n)-(1)/(m)`
`=(m-n)/(mn)`
`rArr " "d=(1)/(mn)`
Put the value of d in eq. (1)
`a+(m-1).(1)/(mn)=(1)/(n)`
`rArr " "a+(1)/(n)-(1)/(mn)=(1)/(n)`
`rArr " "a=(1)/(mn)`
`"Now, "T_(mn)=a+(mn-1)d`
`=(1)/(mn)+(mn-1).(1)/(mn)`
`=(1)/(mn)+1-(1)/(mn)`
=1.