Javascript (using External Library) (66 bytes)
n=>_.From(n).Select((v,i)=>_.From(n).Slice(i,i+v).Sum()).ToArray()
Link to lib: https://github.com/mvegh1/Enumerable
Code explanation: _.From is loading the input array into the library, which is basically LINQ for js. Then each item in the array is mapped according to the following predicate: Take the input, and slice it from current item index and take that index plus the current item's value. Then Sum up that subsequence. Convert the result to a native JS array and return it