I need help with inductive reasoning, what is the sum of first 10 counting numbers? help?

Question

I need help with inductive reasoning, what is the sum of first 10 counting numbers? help?

Answer 1

the first 10 counting numbers are

1

2

3

4

5

6

7

8

9

10

sum = 5*11 =55

thanx

Answer 2

Answer: [(10*11)/2] = 55

$--> assume this is Sigma

the question you asked is

$n where n = 1 to 10;

Now $n = n(n+1)/2

Write the numbers from 1 to 10 in this way,

0 +  1 +  2 + 3 +  4 + 5 + 6 + 7 + 8 + 9 + 10      

10+ 9 +  8 + 7 +  6 + 5 + 4 +  3+ 2 + 1 +  0

--------------------------------------...        

10+10+.............................10 (11 times)  Adding vertically

=>(10*11)/2  this is because we want only half of this sum