Some algorithms on stream

We have found that streams are infinite sequence. Hence, streams are used to create mathematical sequences. We find many mathematical series, which are used in day-to-day simulations and mathematical modeling. Some of mathematical series are as follows:

• Arithmetic progression

• Geometric progression

• Harmonic progression

• Fibonacci series

Brownian motion path

Let us explore some mathematical series using lazy sequences. I should start with the Arithmetic series.

Arithmetic progression

Arithmetic progression is a mathematical sequence where the difference between two consecutive elements is constant:

2, 5, 8, 11, 14, 17,...

The preceding mathematical sequence is an arithmetic progression, and the difference between any two consecutive elements is three. This constant difference is known as common difference. First term of the series is known as initial term. If 1 is the initial term of an arithmetic progression, then the n^th term a_n is calculated as follows:

a_n = a₁ + (n-1...