I was just not understanding how to tackle this sort of problem. I instantly get overwhelmed with number sequences, and I am not understanding the thought process of discovering the pattern with the sequence.

I also had a hard time with it .
But I took the solution like this .
Just solve for 3-4 terms instead of 100 terms and find the answer . The answer will be 3/4(for first 3 terms).
This 4/5 for 4 terms etc.
now you can see that the pattern is the division of two numbers in the last term . i.e
1/1×2 + 1/2×3 + 1/ 3×4 = 3/4.
1/1×2 + 1/2×3 + 1/ 3×4 + 1/4x5 = 4/5 .
so 1/1×2 + 1/2×3 + 1/ 3×4… 1/99*100 = 99/100.

Thats one way .
Another common pattern is to make the terms cancel out and be left with two terms only.
I saw so many sequence problems to use this .
like we can write question as
(2-1) / 1x2 + (3-2)/2x3 +… ans so on . now if we distribute the denominator to each number in numerator .
It will become
1 - 1/2+1/2 - 1/3 + 1/3 … - 1/100 = 99/100 < - we can see here that most terms will cancel out.

Other than these two ways, I am not so sure either if there is a better way to solve these types.