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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Sequences and Series

NDA 2018 · Mathematics · Sequences and Series

Let T_r be the r^ th term of an AP for r=1,2,3, If for some...

Let TrT_r be the rth r^{\text{th }} term of an AP for r=1,2,3,…r=1,2,3, \ldots If for some distinct positive integers m and n we have Tm=1/n\mathrm{T}_{\mathrm{m}}=1 / \mathrm{n} and Tn=1/m\mathrm{T}_{\mathrm{n}}=1 / \mathrm{m}, then what is Tmn\mathrm{T}_{\mathrm{mn}} equal to?

Options

  1. A(mn)−1(\mathrm{mn})^{-1}
  2. B\mathrmm−1+nn−1\mathrmm^{-1}+\mathrm{nn}^{-1}
  3. C1
  4. D0

Correct answer

C. 1

Step-by-step solution

Tn=1m,Tm=1n⇒1st term = c.d. =1mn⇒Tmn=1mn+mn−1mn=1\begin{aligned} & \mathrm{T}_{\mathrm{n}}=\frac{1}{m}, \mathrm{ T}_{\mathrm{m}}=\frac{1}{n} \\ \Rightarrow \quad & 1^{\mathrm{st}} \text{ term }=\text{ c.d. }=\frac{1}{m n} \\ \Rightarrow & \mathrm{ T}_{m n}=\frac{1}{m n}+\frac{m n-1}{m n}=1\end{aligned}
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