1-2+3-4+5-6+.+99-100怎么算最简便

2024-12-04 11:48:20
推荐回答(5个)
回答1:

1-2+3-4+5-6+...+99-100=-50有两种简便算法:

1、直接加减法。

1-2=-1;3-4=-1;5-6=-1直到99-100=-1,因为有100个数,每2个数一组,故一共有50组差为-1

的数,即  1-2+3-4+5-6+...+99-100

=(1-2)+(3-4)+(5-6)+...+(99-100)

=-1 x 50

=-50  

2、等差数列算法。

把相加的数先加起来,即1+3+5+7+...+99,要减的数也加起来,2+4+6+...+100,两者再相减即

可。等差数列的公式是:【(首项+末项)x 项数】/2,其中项数=(后项-前项)/公差+1,即

1+3+5+7+...+99的项数是(99-1)/2+1=50,2+4+6+...+100的项数是(100-2)/2+1=50,故

1-2+3-4+5-6+...+99-100

=(1+3+5+7+...+99)-(2+4+6+...+100)

=(1+99)x50/2-(2+100)x50/2

=2500-2550

=-50

扩展资料:

等差数列的算法:等差数列是常见数列的一种,可以用AP表示,如果一个数列从第二项起,每一项

与它的前一项的差等于同一个常数,这个数列就叫做等差数列,而这个常数叫做等差数列的公差,

公差常用字母d表示。

例如:1,3,5,7,9……(2n-1)。等差数列{an}的通项公式为:an=a1+(n-1)d。前n项和公式为:首项

×项数+【项数(项数-1)×公差】/2或【(首项+末项)×项数】/ 2。

回答2:

1-2+3-4+5-6+.+99-100
=(1-2)+(3-4)+(5-6)+……+(99-100)
=(-1)+(-1)+(-1)+……+(-1)
=(-1)×100÷2
=-50

回答3:

1-2+3-4+5-6+...+99-100
=(1-2)+(3-4)+(5-6)+...+(99-100)
=-1-1...-1
=-1x50
=-50

回答4:

=(-1)×50
=-50

回答5:

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