Question
Sum of the series n . 1 + (n - 1). 2 + (n - 2) . 3 + ........ + 1. n
Solution
The given series is: n. 1 + (n - 1) . 2 + (n - 2) . 3 + ............. + 1. n
Let Tk denote its kth term
∴ Tk = [kth term of n, n - 1, .....] 
[kth term of 1, 2, 3, ........]
= [n + (k - 1) (-1)] [1 + (k - 1)1] = (n - k + 1) (k) = nk - k2 + k
Tk = (n + 1)k - k2
Let 
denote the sum of the series
∴ 
= 
= 
