so given is:
1. T(n)= T(n-1) + n
2. T(0)= 1
so it gets like this:
T(0) = 1
T(1) = T(0) + 1 = 2
T(2) = T(1) + 2 = 4
T(3) = T(2) + 3 = 7
T(4) = T(3) + 4 = 11
T(5) = T(4) + 5 = 16
if you look closer it is:
T(k) = sum(k) +1 // sum(k)=1+2+3+4+5 ... + k-1+k
Take a look at Gauss The sum of all natural numbers, he told us, that sum(k)=(k^2+k)/2
so your solution should be:
T(k) = 1 + (k^2+k)/2