Let $T_{r}$ be the $r^{t h}$ term of an A.P, for r=1, 2, 3,-------. If for some positive integers m,n we have $T_{m} = \frac{1}{n}$ and $T_{n} = \frac{1}{m}$ , then $T_{m n}$ =

Q. Let

T_{r}

be the

r^{t h}

term of an A.P. for

r \in N

. If for some positive integers

m

and

n

, we have

T_{m} = \frac{1}{n}

and

T_{n} = \frac{1}{m}

, then

T_{m n}

is equal to

Q. Let

T_{r}

be the

r^{t h}

term of an A.P. for

r = 1, 2, 3, \dots

If for some positive integers

m, n

T_{m} = \frac{1}{n}

and

T_{n} = \frac{1}{m}

, then

T_{m n}

equals

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Let Tr be the rth term of an A.P for r= 1,2,3,......... If for some positive integers m,n we have Tm=1n and Tn=1m , then Tmn is equal to

The correct option is C 1Let Tm=a+(m−1)d=1n ........(1)and Tn=a+(n−1)d=1m ........(2)On subtracting eqn(2) from eqn(1), we get(m−n)d=1n−1m=m−nmn⇒d=1mnAgain,Tmn=a+(mn−1)d=a+(mn−n+n−1)d=a+(n−1)d+(mn−n)d=Tn+n(m−1)1mn=1m+m−1m=1

Let $T_{r}$ be the $r^{t h}$ term of an A.P for r $=$ 1,2,3,......... If for some positive integers m,n we have $T_{m} = \frac{1}{n}$ and $T_{n} = \frac{1}{m}$ , then $T_{m n}$ is equal to