Fun trick I learned for adding consecutive numbers (1 to 100, in this case). You find the average of the largest and smallest numbers added together, then just multiply the average by the numbers of terms in the sequence. So, in this case, add the smallest and largest (1+100=101), and find their average (50.5). Multiply that by the total number of terms (100, in this case). So 50.5 x 100 = 5050.
On the first day of Christmas, my true love gave to me... The multiplicative identity! On the second day of Christmas, my true love gave to me... The only even prime, and the absolute value of e to the i pi! etc. etc. etc.
According to legend, Gauss figured this out for himself when he was age 10 or so, when his teacher gave him the assignment as a punishment for talking in class.
Ah, that's another way to do it. I just knew that 0+100=100, 1+99=100, ..., 49+51=100, so that's 50 terms that equal 100, so that's 5000 plus the 50 that was left over.
I did this by the AP formula :
n/2[2a+(n–1)d], where 'a' is the first number of the AP, 'd' is the difference between the numbers, and 'n' is the amount of numbers in the AP
I hope you know where the formula comes from! It comes from the description given above, only with the first term (a) and the last term (a + (n-1)d) re-written.
@roleybob why, if someone reads the question correctly, there is allways someone that feels the need to put them down and called them pedantic. (In SOME cases people are being too difficult, but sometimes the question is really asking for something else, where it isnt obvious that a generalisation is used for instant. Like weight and mass, obviously not the same, but you know what is meant)
I just retook this quiz, only this time I noticed the link between the country south of Panama and the province north of Washington. In fact this time I spelt the latter the same way as I spelt the other one, which was fortunately accepted!
Isn't the answer 4949 since it says the numbers BETWEEN 1 and 100. That means that 1 and 100 are excluded otherwise the question should be What is the sum of the numbers between 0 and 101.
John Winger: Why'd the chicken cross the road?
Soldiers: To get from the left to the right
John Winger: He stepped out of rank, got hit by a tank
Soldiers: He ain't no chicken no more
To get to the other side..