Can I update from 7.34 to 7.41 directly? What is the safest way to do so? I have a site built using Drupal 7.34, and now I want the core to be upgraded to 7.41 and would like to know the safest way to do it.
Yes, Drupal Core is self-contained in that any forward version of Drupal contains all the updates of intermediary versions of Drupal you are missing. So, you don't have to install and update Drupal manually through every single version of Drupal that is released.

The recommended way is to simply overwrite your drupal site files as per the distributed documentation with Drupal. Put your site in Maintenance Mode and run the update script.

Alternatively, you can upgrade Drupal via Patches:
https://fuerstnet.de/en/drupal-upgrade-easy-way