Sequences and Series — MATHS STD 11 Science — Question

Given: a₁ = a₂ = 2, a_n = a_n-1 - 1, n > 2
Putting n = 3, 4 and 5, we get
a₃ = a_3-1 - 1 = a_{2 - 1} = 2 - 1 = 1
a₄ = a_4-1 - 1 = a_{3 - 1} = 1 - 1 = 0 
a₅ = a_5-1 - 1 = a_{4 - 1} = 0 - 1 = -1
Hence the first five terms are 2, 2, 1, 0, -1.
Therefore, corresponding series is 2 + 2 + 1 + 0 + (-1) + .......