Question

IM CONFUSED Look at the table. Make a conjecture about the sum of the first 10 positive even numbers. SEE PHOTO

Answer 1

pay attention to pattern in last column

Answer 2

sum of first `1` even numbers = `1*2`
sum of first `2` even numbers = `2*3`
sum of first `3` even numbers = `3*4`
...

see any pattern ?

Answer 3

good question !

Answer 4

what do you think about the sum of first `100` even numbers ?

Answer 5

So cute

Answer 6

she is offline :o

Answer 7

Ikram you should get the title "ice breaker" since you make every question so fun :3

Answer 8

:D to manny titles for today :3
im satisfied with Mrs bond

Answer 9

too :P

Answer 10

Miss Bond that breaks the ice and is also nicknamed marki :3, long title but yeah :D

Answer 11

Is that why you have 002 in your name, 002 bond...ikram bond..

Answer 12

lol sort of :P

Answer 13

I guess @mathisopeningmypath is gone :c

Answer 14

yeah she is offline :o

Answer 15

wait lol thats not her name xD

Answer 16

;)

Answer 17

I fixed it

Answer 18

:P much better

Answer 19

Ganeshie must be eating or something :P

Answer 20

lol ok i see it

Answer 21

nice :) so whats the pattern ?

Answer 22

they are multiples of 2

Answer 23

thats a very good statement for a conjecture !

Answer 24

lets see if we can do better..

Answer 25

ok

Answer 26

take a good look at below :

sum of first `1` even numbers = `1`*2
sum of first `2` even numbers = `2`*3
sum of first `3` even numbers = `3`*4
...

Answer 27

Notice that the sum can be obtained by manipulating the "number of terms"

Answer 28

for example :

if you have `100` numbers, the sum would be : `100`*101

Answer 29

\[\sum _{n=1}^{10} 2 n=2 \sum _{n=1}^{10} n \]