(1-1/2^2)(1-1/3^2)(1-1/4^2)…(1-1/10^2)

(1-1/2^2)(1-1/3^2)(1-1/4^2)…(1-1/10^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)...(1-1/10)(1+1/10)
=(1/2)*(3/2)*(2/3)*(4/3)*(3/4)*(5/4)*.(9/10)*(11/10)
=1/2*11/10
=11/20
100^2-99^2+98^2-97^2+96^2-95^2+…+4^2-3^2+2^2-1^2
=(100-99)(100+99)(98-97)(98+97).(2-1)(2+1)
=100+99+98+97+...+2+1
=5050