1 Sum of first n natural numbers = n(n+1)2
[Formula.]
2 Arthmetic mean of first n natural numbers = Sum of the numbers n
[Formula.]
3 = n(n+1)2n = n+12
4 So, the Arthmetic mean of first n natural numbers = n+12
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Algorithm to find the sum of first n natural numbers:1. Read n.2. Initialize N=1.3. Initialize sum S=0.4. Calculate S=S+N.5. Calculate N=N+1.6. If N>n, then goto step 7 else goto step 4.7. Write the sum S.8. Stop.
Well, you can look it up yourself in a table of prime numbers. But the general tendency is that, the higher you go, the less prime numbers you'll find in each interval. The long-term tendency is that among the first "n" numbers, you'll find n / ln(n) prime numbers, where ln(n) is the natural logarithm. This formula is not terribly accurate for small numbers, but it gets better and better as "n" gets larger.
The set of natural numbers or counting numbers N is a subset of the set of real numbers R. N = {1, 2, 3, ...) R = {..., -2, -1, -0.5, 0, 1, √2, 2, 3, π, ...}
The general equation to find the sum of the numbers 1 to n is: (n*(n+1))/2So, for n=10, you have:(10*(10+1))/2(10*11)/2110/255
Let n = smallest of the odd numbers, then let n+2 = the larger of the two numbers (Remember, 1 is not a prime number.) n+ n+2 = {(2)(7)}2 2n +2 = 142 2n = 196 -2 2n = 194 n = 97 n + 2 = 99