Sequence And Series Question 177
Question: Let $ T_{r} $ be the $ r^{th} $ 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 equals
[IIT 1998]
Options:
A) $ \frac{1}{mn} $
B) $ \frac{1}{m}+\frac{1}{n} $
C) 1
D) 0
Show Answer
Answer:
Correct Answer: C
Solution:
$ T_{m}=a+(m-1),d=\frac{1}{n} $ and $ T_{n}=a+(n-1),d=\frac{1}{m} $ On solving $ a=\frac{1}{mn} $ and $ d=\frac{1}{mn} $
$ \therefore $ $ T_{mn}=a+(mn-1),d=\frac{1}{mn}+(mn-1)\frac{1}{mn}=1 $
BETA
