Question

用平方差公式计算2道1:100^2-99^2+98^2-97^2.+2^2-1^22:(1-1/2^2)乘(1-1/3^

Answer 1

100^2-99^2+98^2-97^2.+2^2-1^2

=(100+99)(100-99)+(98+97)(98-97)+……+(2+1)(2-1)

=100+99+98+……+2+1

=100*(100+1)/2

=5050

(1-1/2^2)乘(1-1/3^2)乘(1-1/4^2)...乘(1-1/9^2)乘(1-1/10^2)

=(1-1/2)*(1+1/2)*(1-1/3)*(1+1/3)*……*(1-1/10)*(1+1/10)

=(1/2)*(3/2)*(2/3)*(4/3)*……*(9/10)*(11/10)

中间约分约去

=(1/2)*(11/10)

=11/20