Write an algorithm for the following:

1.) Algorithm to find out the Sum of Series 1^2 + 2^2 + + n^2

2.) Algorithm to determine the LCM and GCD of two given numbers.

3.) Algorithm to find a Factorial of a number using recursion.

4.) Algorithm to display Prime numbers between two intervals.

5.) Algorithm to check whether a number is Palindrome or not

6.) Algorithm to generate Fibonacci series within a range

7.) Algorithm to find largest and smallest element of an array.

8.) Algorithm to sort a set of numbers in ascending order and to search an item in that set.

9.) Algorithm to multiply to Matrix using multi-dimensional arrays.

10.) Algorithm to append text to an existing file.