Question

How do you find the partial sum of `sum_(r=0)^(100)(8-3r)/16` ?

Answer 1

`sum_(r=0)^100= -896.375`

Explanation:

`sum_(r=0)^100=(8-3r)/16= sum_(r=0)^100 8/16 - (3r)/16`

`=sum_(r=0)^100 1/2 -3/16* sum_(r=0)^100 r` or

`[sum_(r=0)^n=(n(n+1))/2]`

`sum_(r=0)^100=1/2*101 - 3/16* (100*101)/2`

`sum_(r=0)^100=50.5 - 3/16* 5050` or

`sum_(r=0)^100=50.5 - 946.875= -896.375` [Ans]