Find a closed form for these summations?

Question

Find a closed form for these summations?

    n=100
a) ∑ 1/2
     i=1

     n=5
b) ∑ 1/3
     i=1

Answer 1

Adding N of the same number X together is the same as multiplication (you get NX)

 

Also note if you sum f(n) from n=a to n=b, there are b-a+1 terms

 

a) You are adding 100 copies of 1/2 so you get 100 · 1/2 = 50

 

b) You are adding 5 copies of 1/3 so you get 5 · 1/3 = 5/3