Compute the sum (a +(2n+1)d)^2- (a + (2n)d)^2 +(a + (2n-1)d)^2 - (a+(2n-2)d)^2 + ... + (a+d)^2 - a^2
I am confused, how can I figure out the number of terms from here? I know that it decreases by d with each term. But I don't know that number of terms. How does 2n-1 become 0?
Notice that the coefficient of d decreases:
2n + 1, 2n, 2n - 1, 2n - 2, ... 1
The way that the coefficient can become one if the coefficient is '2n - '
so that '2n -
If 'something' is '2n - 1' then 2n - (2n- 1) = 2n - 2n + 1 = 1.