Question

if the mth term of an a.p. be 1/n and nth term be 1/m,then show that its (mn)th term is 1
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Answer 1

Step-by-step explanation:

A/Q, 1/n=a +(m-1)d [1]

1/m=a+(n-1)d [2]

[1]-[2]

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

=>m-n/mn =md-nd

=>d=1/mn

from [1],

1/n=a+(m-1)×1/mn [since d=1/mn]

=>1/n=a+1/n-1/mn

=>a=1/mn

therefore, mnth term =a+(mn-1)×1/mn

=1/mn+1-1/mn

=1

proved.

Answer 2

Answer:

A/Q, 1/n=a +(m-1)d [1]

1/m=a+(n-1)d [2]

[1]-[2]

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

=>m-n/mn =md-nd

=>d=1/mn

from [1],

1/n=a+(m-1)×1/mn [since d=1/mn]

=>1/n=a+1/n-1/mn

=>a=1/mn

therefore, mnth term =a+(mn-1)×1/mn

=1/mn+1-1/mn

=1

proved.