Question

If a1,a2,…,a100 are real numbers such that a1=1 and a100=.01, evaluate ∑(j=1 to 99) (aj−aj+1).

Answer 1

take a look at the sum

(a1-a2)+(a2-a3)+...+(a98-a99)+(a99-a100)
Everything cancels out except
a1 - a100