Find a Sum of a series

Can you tell me how to calculate
f(n)=f(n-1)+n^5
f(0)=1
without using recursive
Thank you

Quote:

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Originally Posted by Kawaguchi

Can you tell me how to calculate
f(n)=f(n-1)+n^5
f(0)=1
without using recursive
Thank you

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In a for() loop?

But how :(?

Maybe like this:

Code:

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int func(int n)
{
    int res = 1;
    while (n > 0)
    {
        res += n*n*n*n*n;
        n--;
    }
    return res;
}

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- petter

As VladimirF said. A for loop. Complete untested ..

Code:

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template< typename T >
std::vector < T >
sum_of_series ( std::vector < T >& in )
{
  std::vector < T > out;
  typedef std::vector < T >::size_type  size_type;
  size_type const sz = in.size ();
  if ( ! sz  )
    //  throw ();  // do something ..

  out.resize ( sz );
  out [  0 ] = 1;
  for ( size_type n( 1 ); n< sz; ++n)
  {
      out [ n ] = in [ n - 1 ] + ::pow ( n, 5 ) ;
  }
  return ( out );
}

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You could even modify code to do things inplace..

...or build a lookup table for performance.

Code:

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int series[] = {1, 2, 34, 277 /* more data here */};

result = series[2];  // Result of  f(2).

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thanks everyone, you know so much :)

Also possible to calculate the series in one go:

Code:

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    int f(int i)
    {
        return
            static_cast<int>(
                + 2 * std::pow(
                        i + 1,
                        6)
                - 6 * std::pow(
                        i + 1,
                        5)
                + 5 * std::pow(
                        i + 1,
                        4)
                - 1 * std::pow(
                        i + 1,
                        2)
                ) / 12 + 1;
    }

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Hope this helps

Just for the fun. You can use recursion in Meta-template programming to let the compiler generate the value for you as long as recursion in compile-time is okay as compare to recursion in run-time. :)

Code:

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#include <iostream>
using namespace std;

template<int n>
class Series
{
public:
        static int get()
        {
                return Series<n-1>::value() + n*n*n*n*n;
        }
};


template<>
class Series<0>
{
public:
        static int value()
        {
                return 1;
        }
};

int main()
{
        cout << Series<3>::value();  // f(3)
}

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