1.

If the Tm term of AP be 1/n and Tn term is 1/m,Show that its Tmn term is 1​

Answer»

EXPLANATION.

  • GIVEN

Tm = 1/n

Tn = 1/m

SHOW THAT Tmn = 1

Tm = a + ( m - 1 ) d = 1/n .....(1)

Tn = a + ( n - 1 ) d = 1/m .......(2)

from EQUATION (1) and (2)

we get,

( m - n) d = (1/n - 1/m )

d = 1/NM

put the VALUE of d = 1/nm in equation (1)

we get,

a + ( m - 1 )1/nm = 1/n

a + m / nm - 1/nm = 1/n

a = 1/nm

Therefore,

Tmn = a + ( mn - 1 ) d

1/nm + ( mn - 1) 1/nm

1/nm + mn / nm - 1/nm

Tmn = 1

Hence proved

NOTE = ALSO SEE THE ATTACHMENT OF THIS ANSWER.


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