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Assuming it increases 10 each level, I managed to derive a formula that will determine how many exclusive skill fragments you will need to reach a certain level.
You will need 5n^2 + 25n exclusive skill fragments to upgrade to level n.
I can prove this mathematically. If you don't believe me, here is a brute force example using Excel that might be more convincing.
Now, divide that number by the number of fragments you expect to get per day, and you will have the number of days it will take to get to level n.
So, to reach level 70 you will need 5 * 70^2 + 25 * 70 = 26250 fragments. If you expect to get 20 per day, it should take 26250 / 20 ~= 1313 days. However, that's not all you get from the 10x silver, so that's only the worst case. I am guessing they are getting this 200-days-to-get-to-level-70 business by assuming that you are getting a 100 stack extra at least once per day because 26250 frags / 120 frags per day ~= 219 days.
It gives 24 points per 10x silver in the point bar, so per day, that could be getting 240 points without spending gold. 10000 / 240 ~= 42. Every 42 days, you could get 1000 frags from the point shop.
Getting 1000 frags every 42 days averages to about 23 extra frags per day, so it's like expecting 43 frags per day at minimum. Thus, going that route, the worst case is really 26250 / 43 ~= 610 days to get to level 70. Again, this excludes any bonuses.
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