Find how much is 1 added to 100?
1+2+3+4+5+6+7+8+9+10+…+100
=100×(100+1)2
=50×101
=5050
Because 1+100=2+99=3+98=4+96= ……=50+51=101, so there are 1+2+3+……+100=50*101=5050
Here the formula for summation of an equivariant series is utilized.
The formula is: (first term + last term) x number of terms ÷ 2 = sum of the series.
According to the formula formula: (1 + 100) × 100 ÷ 2 = 5050
Explanation: the first term in the formula can be interpreted as the series of “the first number”; formula in the end of the formula can be interpreted as “the last number”; the number of terms in the formula is actually the “last number”; the number of terms in the formula is actually the number of terms in the series of “the first number”. The number of terms in the formula is actually the “number of the series”.
Expansion:
What is 1 added to 100? Detailed algorithm
1 plus to 100 formula derivation process: 1+2+3+4+5+6+7+8+9+10+11+….. .90+91+92+93+94+95+96+97+98+99+100
=(1+100)+(2+99)+(3+98)+(4+97)+(5+95)+…… (47+54)+(48+53)+(49+52)+(50+51)
=101+101+101+101+101+…… +101+101+101+101 (50 101s in total)
=50×101
=5050
Thus we get the easy algorithm: 1+2+3+4+5+6+7+8+9+10+11+….. .90+91+92+93+94+95+96+97+98+99+100
=(1+100)×100÷2
=50×101
=5050
ￌ
1 plus to 100 is actually the summation of an equivariant series with the first term = 1, the final term = 100, there are 100 terms in total, and it is easiest to use the formula directly, and = (first term + final term) × number of terms ÷ 2.
Expanded information:
Other derived formulas for the equivariant series:
1, and = (first term + final term) × number of terms ÷ 2.
2, number of terms = (final term – first term) ÷ tolerance + 1.
< p>3. First term = 2x and ÷ number of terms – last term or last term – tolerance x (number of terms – 1).
4. Last term = 2x and ÷ number of terms – first term.
5. End term = first term + (number of terms – 1) x tolerance.
6. 2(first 2n terms and – first n terms and) = first n terms and + first 3n terms and – first 2n terms and.
What is the sum of adding from 1 to a hundred? Is there any formula?
The sum is 5050, there are three formula algorithms;
The first and most common is the most familiar addition formula: 1+2+3… +100 = 5050, just add them all.
The second is the sum of the equivariant series formula: n * (n + 1)/2 = 100 * 101/2 = 5050.
The third is the Gaussian algorithm formula: the first plus the last term multiplied by the number of terms divided by 2 is used to calculate the “1 + 2 + 3 + 4 + 5 + — + (n – 1) + n” =. (1+100)+(2+99)+… +(50+51)=101*50=5050
Information Expanded
Origin of Gauss’s Algorithm
On one occasion in a math class, the teacher asked the students to practice counting. So he asked them to count the number of 1+2+3+4+5+6+……+100 in an hour.
Only Gauss in the class gave the answer in less than 20 minutes, because he figured out that with (1+100)+(2+99)+(3+98)……+(50+51)…… there are 50 101s, so 50 x 101 is the number of 1’s added to a hundred. Later people called this easy algorithm Gaussian algorithm.
Gauss
JohannCarlFriedrichGauss (April 30, 1777-February 23, 1855)
Gauss is listed as one of the world’s top three mathematicians along with Archimedes and Newton. His life’s accomplishments were extremely fruitful, and the number of results named after him “Gauss” reached 110, which is the most among mathematicians.
Gauss was a famous German mathematician, physicist, astronomer, geodesist, and one of the founders of modern mathematics, and is considered one of the most important mathematicians in history, and enjoys the name of “Prince of Mathematics”.
He contributed to number theory, algebra, statistics, analysis, differential geometry, geodesy, geophysics, mechanics, electrostatics, astronomy, matrix theory, and optics.
1 plus to 100 is equal to how much can be calculated in what way
1, 1 plus to 100 is equal to 5050. in fact, to use some simple methods to calculate, 1 plus to 100 is equivalent to 50 101, and then directly multiplied with it will be able to get a specific number, the answer is 5050.
2, Gaussian summation formula. That is, the sum of the equivariant series, “and = (first + last) × number of terms / 2”, so you can get (1 + 100) * 100 / 2 = 5050.