The literal expression of oxygen production from hydrogen peroxide solution

The literal expression of oxygen production from hydrogen peroxide solution

Hydrogen peroxide arrow (manganese dioxide on the arrow) water + oxygen

Chemical reaction of hydrogen peroxide and manganese dioxide to produce oxygen

Hydrogen peroxide → manganese dioxide water + oxygen (manganese dioxide is written above the arrow)

In VB, let x = 5 and the expression "10"

This expression, starting from left to right, is easy to understand
1. First 10

There are 1 cube in the first layer, 3 cubes in the second layer, 6 cubes in the third layer, 10 cubes in the fourth layer, and s cubes in the nth layer. When n = 10, what is s?

The first layer is one
The second layer is 1 + 2 = 3
The third layer is 1 + 2 + 3 = 6
The fourth layer is 1 + 2 + 3 + 4 = 10
.
The nth layer is s = 1 + 2 + 3 +. + n = n (n + 1) / 2
When n = 10, s = 1 + 2 + 3 +... + 10 = 10 (10 + 1) / 2 = 55

The cube with edge length a has n layers, including 1 cube in the first layer, 3 cubes in the second layer, 6 cubes in the third layer and 10 cubes in the fourth layer

Let the nth layer have an, then A1 = 1, an = a (n-1) + N, so an = a1 + (a2-a1) + +(an-a(n-1))
=1+2+…… +n=n(n+1)/2
Sn = (1 / 2) [n (n + 1) (2n + 1) / 6 + n (n + 1) / 2] = n (n + 1) (n + 2) / 6, that is, there are n (n + 1) (n + 2) / 6 in the first n layers

How many cubes are there in the tenth layer? One in the first layer, three in the second layer, six in the third layer, and so on?
There is one on the first floor, three on the second floor and six on the third floor

1
1+2
1+2+3
...
1+2+...+10=(1+10)*10/2=55

From 1, 2, 3, 4, 5, 6, 7, 8, 9, which number is an integral multiple of 3, which number is an integral multiple of 2?

3: 3 6 9 2: 2

If a = 1 + 1 / 2 + 1 / 3 + 1 / 4 + 1 / 5 + 1 / 6 + 1 / 7 + 1 / 8, what is the integer part of a?

First, 1 / 2 + 1 / 4 + 1 / 8 = 7 / 8,
1/3+1/6+1/5=1/2+1/5=7/10,
A=1+1/2+1/3+1/4+1/5+1/6+1/7+1/8
=1+(1/2+1/4+1/8)+(1/3+1/6+1/5)+1/7
=1+7/8+7/10+1/7
Because: 1 / 7 > 1 / 8
2

Find the simplest integer ratio 1.1/6:1 / 7:1 / 8 2,3 / 4:2 / 5:2 / 3

1/6：1/7：1/8
=28：24：21
3/4:2/5:2/3
=45：24：40

1 + 2-3-4 + 5 + 6-7-8 + is a series of numbers written down by taking two positive and two negative integers from 1
1 + 2-3-4 + 5 + 6-7-8 + 9 + 10-11-12 is a series of numbers written down by taking two positives and two negatives from the continuous integers starting from 1. What is the sum of the first 2004 numbers? How to calculate it?

There were 501 groups in each group,
The sum of each group is - 4,
Therefore, the sum of the first 2004 numbers is (- 4) * 501 = - 2004