(2+4+6+...+98+100)-(1+3+5+...+97+99)怎么做

问题描述:

(2+4+6+...+98+100)-(1+3+5+...+97+99)怎么做

(2-1)+(4-3)+……+(100-99)
=1 + 1 + ……+1
+50

=2-1+4-3+6-5+。。。+100-99
=1+1+1+。。。+1
=50

奇数和偶数各有50项,都是等差数列
(2+4+6+...+98+100)-(1+3+5+...+97+99)=(2+100)*50/2 - (1+99)*50/2
=50

(2+4+6+...+98+100)-(1+3+5+...+97+99)
=【(92+100)*50/2】-【(1+99)*50/2】
=2550-2500
=50