Q.124. Series

Question 124.
There is a series of numbers denoted by a1, a2, a3, ... aX (Not in Arithmetic Progression!).
Here's what we have:
a1 = 1 and
a(M + N) = aM + aN + MN
Using the two given data, find the 2001st term.

Answer 124.
a(M + N) = aM + aN + MN
Putting M = 1
=> a(N + 1) = a1 + aN + N
=> a(N + 1) - aN = N + 1
Putting N = 1,
=> a(2) - a(1) = 1 + 1
=> a(2) = 3
Putting N = 2,
=> a(3) - a2 = 3
=> a(3) = 6
Thus, series is 1, 3, 6, 10, 15, ....
Thus, a(N) = ΣN
=> a(2001)
= Σ2001
= (2001) * (2002) / 2
= 2003001.

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