Blockchain size problem According to my understanding, the ledger/blockchain is stored on every computer (node) that partakes in the network. The beauty of this system is that it is decentralised and backed up by every single participant in the network. Furthermore, the security of the blockchain comes from there being so many copies, as long as there are many copies, then it's unfeasible for anyone to try to "hack" it, as too many other people have copies which would be automatically checked against your fake one to reveal the deception. On average a new block is created every 10 minutes. Right now there is a limit of 1 MB per block. So, if the limit isn't changed, then the growth rate is limited at:


1 MB every 10 minutes (on average) 
6 MB every hour (on average)
Approximately 144 MB per day 
Just a bit over 1 GB per week 
A bit less than 4.4 GB per month 
A bit less than 52.6 GB per year


How is it feasible for someone with capped internet to participate in the blockchain network as it starts to grow over time? For example, the Internet in third world countries is limited, expensive and slow. Are there any solutions out there or research being carried out which resolve the scalability problem which is currently an inherent property of Bitcoin?
SPV clients are thin clients that do not need to hold the full blockchain. They use other nodes on the network to validate transactions. SPV clients are available for Android and require a lot less disk space. 
Of course it is more secure for you and for the network to run a full node.