Find the value of 1000^2-999^2+998^2-997^2.......+4-1=?

Question

Pawan asks Kashish, 'It is 9 pm as per my watch right now.
Do you know what will be the time 23, 999, 997 hours later?'

Kashish knows the answer. Do you ?

Answer 1

a^2-b^2 = (a+b)(a-b)
so
100^2-99^2=(100+99)(100-99)=100+99

so
1000^2-999^2+998^2-997^2.......+4-1
= 100+99+98+97...1
= 100*101/2
= 101*50
= 5050