1. Tardigrade
  2. Question
  3. Mathematics
  4. Let xn be the sequence of numbers denoted by xn=(195/4 Pn)-( n+3 P3/Pn+1)(n ∈ N) where Pn denotes the number of ways in which n distinct things can be arranged on n different places in a definite order. The sum of all possible values of n ∈ N for which xn>0, is

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Q. Let $x_n$ be the sequence of numbers denoted by $x_n=\frac{195}{4 P_n}-\frac{{ }^{n+3} P_3}{P_{n+1}}(n \in N)$ where $P_n$ denotes the number of ways in which $n$ distinct things can be arranged on $n$ different places in a definite order. The sum of all possible values of $n \in N$ for which $x_n>0$, is

Permutations and Combinations

Solution:

We must have,
$(2 n +19)(2 n -9)<0 \Rightarrow \frac{-19}{2}< n <\frac{9}{2} \Rightarrow n \in\{1,2,3,4\}$
Hence, sum $=1+2+3+4=10$