Changes

The sum of finite series is ingenral relativly straight forward to calculate it consist of mearly summing together all the numbers in a sequences. However this can be time consumming and in pre-computer mathematics many shortcuts were found.

The sum of finite series is ingenral relativly straight forward to calculate it consist of mearly summing together all the numbers in a sequences. However this can be time consumming and in pre-computer mathematics many shortcuts were found.

Gauss once famously was given the assignment by his teacher to add the number between 1 and 100. The rest of the students were working hard and after less than a minute he correctly wrote 5050. This story whilst is allogorical leads to a key insight in finite sums,

Gauss once famously was given the assignment by his teacher to add the number between 1 and 100. The rest of the students were working hard adding carefully, but after less than a minute he correctly wrote 5050. This story whilst is allogorical leads to a key insight in finite sums,

:<math>\sum^{N}_{n=1}n=\frac{N(N+1)}{2}</math>

:<math>\sum^{N}_{n=1}n=\frac{N(N+1)}{2}</math>