Second floor: 3=2×(2+ 1)÷2
Layer 3: 6=3×(3+ 1)÷2
The fourth floor: 10=4×(4+ 1)÷2.
……
N layer: n×(n+ 1)÷2
So 100 floor has:
100×( 100+ 1)÷2
= 100× 10 1÷2
= 10 100÷2
=5050 (pieces)
The whole pile of * * * has:
( 1+5050)× 100÷2
=505 1× 100÷2
=505 100÷2
=252550 (pieces)
A: When the number of layers is 100, there are 252,550 balls in the whole pile.