How many terms are in the series
1, 2, 2, 3, 3, 3, 4, 4, 4, 4,........,20,....twenty times 20...., 20
I tried a few things- the most promising way I found is by taking the above as:
1, 4, 9,...., 20^2
where nth term is n^2, thinking somehow later I could add up the number of terms which I combined and reduced by forming another special series but I couldn't figure it out.
This is actually number of rounds of running a block I want to go for each day.
Sum of $n$ first terms is $$\sum_{i=1}^ni=\frac{n(n+1)}{2}$$
There are $$1+2+...+(20) $$terms in the series..So put $n=20$ in above formula
$$20(21)/2=210$$ So there are $210$ terms in total