maths_and_science: Assignment for December 25

Squares of Numbers :

   Finding Sum without "Adding the numbers."
            1+2+3+4+5+6+7+9+10+11+12+13

    I can either add 1+2+3... upto 13 and tell the sum,
    OR
    I can count the number of items in that line ( i.e there are 13 items )
        Now, that I know there are 13 items - Just square it.
        13 square is 169. ( so the answer is 169)

    Having read this please solve the problems below

Problems:
            1+2+3+4+5+6+7+9+10+11+12+13+15+17

            1+2+3+4+5+6+7+9+10+11

Triangular Numbers :

Triangular Numbers are defined as :

1                    = 1
1+2                = 3
1+2+3            = 6
1+2+3+4        = 10
1+2+3+4+5    = 15

Here 1, 3, 6, 10 and 15 are called Triangular numbers.

The nth number of the series of triangular number is given by   n ( n+1 )
                                                               --------
                                                                      2
e:g :
        if I were to add 1 + 3, I get 4 = 2 square, i,e '2' is the higher number (look at second line)

Having read this, Solve the problems below.

Problems :
    What is the 6th triangular number ? ( I have already given the 5 triangular numbers above )
     What is the 8th triangular number ?
     What is the 11th Triangular number ?