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
Answers
Answered by
6
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.
Answered by
0
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.
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