Explain Binary Indexed Trees (Fenwick Trees) and their applications.

Fenwick Trees support prefix sum queries and point updates in O(log n) with O(n) space, simpler than segment trees. Each index i stores sum of elements in range determined by lowest set bit of i. Update propagates to indices i + (i & -i); query sums indices i - (i & -i). Can be extended for range updates with point queries, or range updates with range queries using two BITs. Used for cumulative frequency tables and inversion counting.