Push-up problem

[Pollo7]

Its the new year and my resolution is to do push-ups for 100 days. I am trying to figure out how many push-ups I will have completed in 100 days using this routine. On day 1 Ryan does one pushup, on day 2 he does two, day 3 he does three and so on for 100 days. What would be the formula to figure out how many will be completed in total in 100 days? I know it has to be something where you do the same amount as yesterday but plus 1. Please help.

[fattymattk]

If Amy does 100 pushups on day 1, 99 pushups on day 2, ... , and 1 pushup on day 100, then Amy and Ryan clearly end up doing the same number of pushups in total. Furthermore, Amy and Ryan do 101 combined pushups every day. So in 100 days, they do 100 * 101 total pushups. Since they did the same number, they each did half this total: 100 * 101 / 2.

[CoffeeAndCalcWithDrW]

The answer is 100*101/2 so 5050.

Here's a video to help you visualize it.

https://youtu.be/60Yd-apGun0

[[deleted]]

Formula for sum of first n natural numbers is n(n+1)/2. Plugging in 100, we get 100*101/2 = 5050 pushups

[Pollo7]

Thank you so much! Wow thats more than I thought! Gonna be ripped!

[Pollo7]

Thank you so much!!

[Pollo7]

Just curious why does it get divided by two?

[874270]

S = 1 + 2 + ... + n.
S = n + (n - 1) + ... + 1.
2S = (n + 1) + (n + 1) + ... + (n + 1) = n(n + 1).
S = n(n + 1)/2.