If 100 more than the sum of n consecutive natural numbers is equal to the sum of the next n consecutive natural numbers, find n.
Answers
Answer:
Step-by-step explanation:
Sum of natural, odd & even numbers
Sum of “n” natural numbers = \frac{n(n+1)}{2}
Sum of “n” natural even numbers = (n ) (n + 1)
Sum of “n” natural odd numbers = n 2
Sum of square of natural, odd & even numbers
Sum of square of “n” first or consecutive square natural numbers:
Sum of square of "n" first or consecutive square natural numbers | Sum of n Consecutive numbers
Sum of square of “n” first or consecutive odd numbers:
Sum of square of "n" first or consecutive odd numbers | Sum of n Consecutive numbersSum of square of “n” first or consecutive square even numbers:
Sum of square of "n" first or consecutive square even number | Sum of n Consecutive numbers
Sum of cube natural, odd & even numbers
Sum of cube of first or consecutive ” n” natural numbers:
Sum of square of "n" first or consecutive square even number | Sum of n Consecutive numbers
Sum of cube of first or consecutive ” n” even natural numbers = 2n2 (n + 1)2
Sum of cube of first or consecutive ” n” odd natural numbers = n2 (2n2 – 1)
The easy-to-use formula is
(n / 2)(first number + last number) = sum, where n is the number of integers.
Let's use the example of adding the numbers 1-100 to see how the formula works.
Find the sum of the consecutive numbers 1-100:
(100 / 2)(1 + 100)
50(101) = 5,050