Question

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

Answer 1

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.

Answer 2

Step-by-step explanation:

tmn = a+(mn-1)d

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

1/nm + mn/nm- 1/nm

Cancel all

Answer is 1