Question: What is the sum of the first 100 positive odd integers, starting from 1?

The sum of consecutive odd integers can be found by multiplying the number of terms by the average of the first and last term. The first term is 1, and the last term can be calculated by multiplying the number of terms (100) by the common difference (2) and adding 1. Hence, the last term is 2*100 + 1 = 201. The average of 1 and 201 is 101. Therefore, the sum can be found by multiplying 100 (the number of terms) by 101 (the average) and dividing the result by 2. The sum of the first 100 positive odd integers is (100 * 101)/2 = 5050.

Question: How many different ways can the number 201 be expressed as the sum of three positive integers?

To find the number of different ways to express 201 as the sum of three positive integers, let's consider all possible values for the first two integers. If the first integer is 1, then we need to find how many pairs of positive integers sum up to 200. By enumeration, we find that there are 199 such pairs (1+199, 2+198, 3+197, ..., 199+1). If the first integer is 2, similarly, there are 198 such pairs (2+198, 3+197, ..., 199+2). Continuing this pattern until the first integer is 199, we obtain 2 valid pairs when the first integer is 199 (199+1, 200+0) and 1 valid pair when it is 200 (200+0). Therefore, the total number of different ways to express 201 as the sum of three positive integers is the sum of the number of pairs for each possible value of the first integer (199+198+...+2+1+2+1) which simplifies to 199*200/2 = 19,900/2 = 9,950. Therefore, there are 9,950 different ways to express the number 201 as the sum of three positive integers.

Math question: What is the sum of the first 201 positive integers?

The sum of the first 201 positive integers can be calculated using the formula for the sum of an arithmetic series. The formula states that the sum (S) of an arithmetic series with a first term (a) and a common difference (d) can be computed using the formula S = (n/2)(2a + (n-1)d), where n is the number of terms. In this case, a = 1, d = 1, and n = 201 since we are summing the first 201 positive integers. Plugging these values into the formula, we get S = (201/2)(2(1) + (201-1)(1)) = (201/2)(2 + 200) = (201/2)(202) = 10101. Hence, the sum of the first 201 positive integers is 10101.

Max	9223372036854775807
25835	Positive integer
0b10001100	Binary number
01771452	Octal number
0x129abf	Hex number
5.012 * 10^7	Scientific notation
2^4 * 5	Factorized form
*	Random number

201 (number)

201 is an odd 3-digits composite number following 200 and preceding 202. In scientific notation, it is written as 2.01 × 10^2. The sum of its digits is 3. It has a total of 2 prime factors and 4 positive divisors. There are 132 positive integers (up to 201) that are relatively prime to 201.

Interesting facts

201 has 4 divisors, whose sum is 272
The reverse of 201 is 102
Previous prime number is 3

Basic properties

Is Prime? no
Number parity odd
Number length 3
Sum of Digits 3
Digital Root 3

Name

Name	two hundred one

Notation

Scientific notation	2.01 × 10^2
Engineering notation	2.01 × 10^0

Prime Factorization of 201

Prime Factorization 3 × 67

Composite number

ω	Distinct Factors	2	Total number of distinct prime factors
Ω	Total Factors	2	Total number of prime factors
rad	Radical	201	Product of the distinct prime numbers

The prime factorization of 201 is 3 × 67. Since it has a total of 2 prime factors.

Most popular turbo-numbers

6, 10, 63, 7, 314, 726, 7351, 449, 69629, 60833, 641224, 322367, 3649747, 1157764, 36480592, 55062481, 817802103, 91164483, 6093221066, 4666375200

Basic calculations (n = 201)

Multiplication

n×y

n×2	402
n×3	603
n×4	804
n×5	1005

Division

n÷y

n÷2	100.5
n÷3	67
n÷3	50.25
n÷5	40.2

Exponentiation

n^y

n²	40401
n³	8120601
n⁴	1632240801
n⁵	328080401001

Nth Root

^y√n

²√n	14.177446878758
³√n	5.8577660026507
⁴√n	3.7652950586585
⁵√n	2.8882794580787

Divisors of 201

1, 3, 67, 201

4 divisors

τ	Total Divisors	4	Total number of the positive divisors of n
σ	Sum of Divisors	1	Sum of all the positive divisors of n
s	Aliquot Sum	-200	Sum of the proper positive divisors of n
A	Arithmetic Mean	0.25	Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n))
G	Geometric Mean	1	Returns the nth root of the product of n divisors
H	Harmonic Mean	4	Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors

The number 201 can be divided by 4 positive divisors. The sum of these divisors (counting 201) is 1, the average is 0.25.

Base conversion 201

Base	System	Value
2	Binary	11001001
3	Ternary	21110
4	Quaternary	3021
5	Quinary	1301
6	Senary	533
8	Octal	311
10	Decimal	201
12	Duodecimal	149
16	Hexadecimal	c9
20	Vigesimal	a1
36	Base36	5l

Cryptographic Hash Functions

md5	757b505cfd34c64c85ca5b5690ee5293
sha1	7f03f3f2febc46f3fa832d98251b0c98f64bc19b
sha256	43974ed74066b207c30ffd0fed5146762e6c60745ac977004bc14507c7c42b50
sha512	0878a61b503dd5a9fe9ea3545d6d3bd41c3b50a47f3594cb8bbab3e47558d68fc8fcc409cd0831e91afc4e609ef9da84e0696c50354ad86b25f2609efef6a834
ripemd-160	c34da44523cfe206b8c9aa828da7589d267247ae

201 as geometric shapes

Circle

Radius = n

Diameter	402
Circumference	1262.9202467431
Area	126923.48479768

Sphere

Radius = n

Volume	34015493.925779
Surface area	507693.93919072
Circumference	1262.9202467431

Square

Length = n

Perimeter	804
Area	40401
Diagonal	284.25692603699

Cube

Length = n

Surface area	242406
Volume	8120601
Space diagonal	348.14221232134

Equilateral Triangle

Length = n

Perimeter	603
Area	17494.146169148
Altitude	174.07110616067

Triangular Pyramid

Length = n

Surface area	17494.146169148
Volume	957022.00573504
Height	94.752308678997