Patterns in fibonacci Series

 

The Fibonacci Sequence is the series of numbers such that next number is found by adding up the two numbers before it.

Minimum Steiner tree problem

 

Why ? 1-1+1-1+1…..=1/2

The sequence of partial sums of Grandi’s series is 1, 0, 1, 0, …, which clearly does not approach any number.Hence According to Modern mathematics definition of Convergence of Series , Grandi’s series is divergent.

Using the simplest methods other than integration or 1/x method we can prove Grandi’s series is converges to 1/2.

 

RSA cryptography for safe Internet

How our messages can be sent securely in Internet.Here The Number Theory help us to do it.Multiplication of large numbers specifically for this ,the prime numbers is quite easy but what about factoring it?

Sorting methods in Short

Bubble sort

Bubblesort compares adjacent numbers and swap those that are out of order i.e if next number is greater than the previous one then numbers will not swap.This swapping would not stop until  the whole list would get ascending order.

When elements are sorted in reverse order then bubble sort takes maximum time .

When elements are already sorted then  it takes minimum time .
bubble sorted lists are stable.

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