Given an integer N, the task is to find the summation of the harmonic series .
Input: N = 5
floor(3/1) + floor(3/2) + floor(3/3) = 3 + 1 + 1 = 5
Input: N = 20
Naive approach: Run a loop from 1 to N and find the summation of the floor values of N / i. Time complexiy of this approach will be O(n).
Efficient approach: Use the following formula to calculate the summation of the series:
Now, the loop needs to be run from 1 to sqrt(N) and the time complexity gets reduced to O(sqrt(N))
Below is the implementation of the above approach:
- Harmonic Progression
- Harmonic progression Sum
- Leibniz harmonic triangle
- Program for harmonic mean of numbers
- Program to find the Nth Harmonic Number
- Find Harmonic mean using Arithmetic mean and Geometric mean
- Program to find sum of harmonic series
- Summation of GCD of all the pairs up to N
- Series summation if T(n) is given and n is very large
- Find m-th summation of first n natural numbers.
- Arithmetic Progression
- Geometric Progression
- Sum of product of x and y such that floor(n/x) = y
- Ratio of mth and nth term in an Arithmetic Progression (AP)
- Program to print GP (Geometric Progression)
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