Question

the sum of all even numbers from 10 to 50 is​

Answer 1

The sum of all natural number from 1 to n can be computed by the formula (n)*(n+1)/2. It’s easy to visualize the proof of this: suppose n=10. Imagine the number 1 to 10 laid out in front of you. Add 1 and 10 to get 11. Now add 2 and 9 to get 11, 3 and 8 to get 11, 4 and 7 to get 11, 5 and 6 to get 11. How many 11’s did we collect this way? 5. So the sum of the first 10 natural numbers is 5*11 = 55, which is exactly what the formula above says. This trick extrapolates to any sum of consecutive natural numbers starting at 1.

You asked what about the sum of even natural numbers. The sum of even natural numbers between 1 and 2n can be written as the sum of 2*i from i=1 to i=n. Factoring out the 2, it is equal to 2 times the sum of i from i=1 to n. Using the formula for the sum of consecutive numbers, we get that the sum of all even numbers from 1 to 2n equals n*(n+1).

In your case, the sum is through 100 which is 2*50. Therefore the sum of even number to 100 is 50*(51) = 2550

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Answer 2

Answer:

2 + 4 + 6 + 8 + 10 + 12 + .  .  .  .   + 100 = 2550

Step-by-step explanation:

Sum = n/2 x (a + Tn)

=> 50/2 x (2 + 100)

=> (50 x 102)/ 2

=> 5100/2

2 + 4 + 6 + 8 + 10 + 12 + .  .  .  .   + 100 = 2550

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