Here I present solution to two problems posted on Brilliant: Family of 3's and Infinite sum of reciprocal products and provide a solution to the general expressions.
modifying the above one we get,
Putting we get,
Putting we get, the nested radical as in Family of 3's :
Putting we get the infinite series in Infinite sum of reciprocal products:
In fact if and is an integer then,
Using the same nested radicals as above I have derived the following: