Respuesta :
Answer: The Answer is "less than"
Step-by-step explanation:
To find the sum of a series, you find the difference between the first and last term, multiply that by the number of terms, then divide by 2.
For the even numbers, 2 is the first term and 200 is the 100th term (because 2+(100-1)2 is equal to 200). So, (100(2+202)/2 = 10100.
For the odd numbers, 1 is the first term and 201 is the 101th term (because 1+(101-1)2 is equal to 201). So, (101(1+202))/2 = 10251.5.
10100<10251.5 so the sum of the first 100 even numbers is less than the sum of the first odd 101 numbers.
The sum of the first 100 even natural numbers is smaller than the sum of the first 101 odd natural numbers.
What is an even number?
A number that is divisible by two into two equal whole numbers is called an even number. Even numbers are those that end in 0, 2, 4, 6, and 8.
The problem can be solved using the arithmetic sequence. The sum of the first 100 even numbers will be,
[tex]\text{Sum of first 100 even numbers} = \dfrac{100}{2} \times [2(2) +(100-1)2]=10,100[/tex]
The sum of the first 101 odd numbers will be,
[tex]\text{Sum of first 101 odd numbers} = \dfrac{101}{2} \times [2(1) +(101-1)2]=10,201[/tex]
Hence, the sum of the first 100 even natural numbers is smaller than the sum of the first 101 odd natural numbers.
Learn more about Even Numbers:
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