[1] "On average, one broad leaf tree will absorb in the region of 1 tonne of carbon dioxide during its full life-time (approximately 100 years)." http://www.carbonfootprint.com/plantingtrees.html
Ecosia is helping people help the environment. Currently planting trees in Burkina Faso as a part of Great Green Wall.
Full disclosure: I work at Ecosia.
Also a major fraction of trees, ballpark 50+%, have leaves and drop them once a year, and the leaves contribute to topsoil.
Even if a forest burns, the burned trees create ash which has carbon and adds to topsoil.
Some of the topsoil gets washed into rivers and lakes, becomes mud, gets covered over by more mud, and, thus, essentially buries its carbon.
There is more that is similar: a major fraction of the surface of the earth has, within 1000 feet deep, a lot of limestone, and that is partly, largely, or mostly just old sea shells where the animals pulled carbon from the water or what it ate and converted it to calcium carbonate, that is, buried the carbon (disclaimer, I'm no geologist).
In simple terms, basically, net, the earth's biosphere grabs and buries a lot of carbon including CO2 from the atmosphere.
Note: Nowhere here have I made a remark of any kind about the effects on climate of CO2 in the atmosphere.
You'd have to plant 1.6 trees every year, in perpetuity and keep all of them alive for a century.
The obvious solution is to plant an entire forest to ensure that new trees grow to replace old trees.
n CO2 + n H2O + photons → (CH2O)n + n O2
carbon dioxide + water + light energy → carbohydrate + oxygen
Even if the single oxygen per carbon stayed buried, we'd lose a maximum of 400ppm[1] of oxygen, of currently 20.95 % volume of oxygen. That does not even affect the last digit of that rounded number, and the number is normally not given with more digits because it changes with the season and stuff.
No carbon dioxide in the atmosphere would probably be really bad for further tree growth (among other things), so it is naturally limited.