1+2+3+4+.+99用简便方法怎么计算

2024-10-27 16:33:38
推荐回答(5个)
回答1:

1+2+3+4+.+99用简便方法

=(1+99)+(2+98)郑败+...+(49+51)+50

=50*2*49+50

=50*(100-1)

=5000-50

=4950

是等差数列的求和,可以直接求中间的平均值,然后乘以总的数量进行计算。

拓展资料

如果一个数列从第二项起,每一项与它的前裤胡一项的差等于同一个常数,这个数列就叫做等差数列,这个常数叫做等差数列的公差,公差常用字母d表示。等差数列是胡丛拦常见数列的一种。

等差中项即等差数列头尾两项的和的一半.但求等差中项不一定要知道头尾两项。

回答2:

高斯求和: (首项+末项)×项数÷2
=(1+99)×99÷2
=100×99÷2
=9900÷2
=4950
拓展资料:高斯求和
高斯求和
等差数列的通项公式为:an=a1+(n-1)d 前n项和公式为:Sn=na1+n(n-1)d/2或Sn=n(a1+an)/2 注意:n∈N+,d为公差 末项=首项+(项数-1)*公差项数=(末项-首项)/公差+1首项=末项-(项数-1)*公差
例题
1.1+2+3+…+1999=?
分析与解:这串加数1,2,3,…,1999是等差数列,首项是1,末项是1999,共有1999个数。由等差数列求和公式可得原式=(1+1999)×1999÷2=1999000。注意:利用等差数列求和公式之前,一定要判断题目碧猜中的各个加数是否构成等差数列。

2.11+12+13+…+31=?

分析与解:这串加数11,12,13,…,31是等差数列,首项是11,末项是31,共有31-11+1=21(项)。原式=(11+31)×21÷2=441。

在利用等差数列求和公式时,有时项碰卜数并不是一目了然的,这时就需要先求出项数。根据首项、末笑慧穗项、公差的关系,可以得到项数=(末项-首项)÷公差+1,末项=首项+公差×(项数-1)。

3.3+7+11+…+99=?

分析与解:3,7,11,…,99是公差为4的等差数列, 项数=(99-3)÷4+1=25,原式=(3+99)×25÷2=1275。

回答3:

公式:陵答
高斯求和铅嫌:
(首项+末项)×项数÷2
(1+99)槐汪手×99÷2
=100×99÷2
=9900÷2
=4950

回答4:

看下面的图片尺基,陵让谨不需要滑没过多解释,直观:

回答5:

=1+99+(2+98)+(3+97)----+(49+51)+50
=4950

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