Answer:
First, a triangular number can be written as:
Tₙ = (n^2 + n)/2
where n is the number of our triangular number, n = 1 represents the first one, n = 2 represents the second one, etc.
The sum of the first 100 triangular numbers is:
S1 = (T₁ + T₂ + ... + T₉₉ + T₁₀₀)
The sum of the first 99 triangular numbers is:
S2 = (T₁ + T₂ + ... + T₉₉)
Then the difference will be:
D = S1 - S2 = (T₁ + T₂ + ... + T₉₉ + T₁₀₀) - (T₁ + T₂ + ... + T₉₉) = T₁₀₀
And we can find the value of T₁₀₀ if we use the equation for triangular numbers:
T₁₀₀ = (100^2 + 100)/2 = 5,050
