Find nth term of a given recurrence relation in C++

C++Server Side ProgrammingProgramming

Concept

Assume bn be a sequence of numbers, which is denoted by the recurrence relation b1=1 and bn+1/bn=2n. Our task is to determine the value of log2(bn) for a given n.

Input

6

Output

15

Explanation

log2(bn) = (n * (n - 1)) / 2 = (6*(6-1))/2 = 15

Input

200

Output

19900

Method

bn+1/bn = 2n

bn/bn-1 = 2n-1

.

.

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b2/b1 = 21, We multiply all of above in order to attain

(bn+1/bn).(bn/n-1)……(b2/b1) = 2n + (n-1)+……….+1

So, bn+1/b1 = 2n(n+1)/2

Because we know, 1 + 2 + 3 + ………. + (n-1) + n = n(n+1)/2

So, bn+1 = 2n(n+1)/2 . b1; Assume the initial value b1 = 1

So, bn+1 = 2sup>n(n+1)/2

Now substituting (n+1) for n, we get,

bn = 2n(n-1)/2

Taking log both sides, we get,

log2(bn) = n(n-1)/2

Example

 Live Demo

// C++ program to find nth term of
// a given recurrence relation
#include <bits/stdc++.h>
using namespace std;
// Shows function to return required value
int sum(int n1){
   // Now get the answer
   int ans1 = (n1 * (n1 - 1)) / 2;
   //Now return the answer
   return ans1;
}
// Driver program
int main(){
   // Get the value of n
   // int n = 6;
   int n = 200;
   // Uses function call to print result
   cout << sum(n);
   return 0;
}

Output

19900
raja
Published on 25-Jul-2020 14:14:11
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