Find the sum of natural numbers with two digits divisable by

Find the sum of natural numbers with two digits divisable by 11.

Solution

Let\'s discover the set A, composed by the 11 multiplex, numbers formed from 2 digits.

A={11*1,11*2,11*3,11*4,11*5,11*6,11*7,11*8,11*9}

A={11,22,33,44,55,66,77.88.99}

S = (11+2+33+44+55+66+77+88+99)

We\'ll factorize by 11 and w\'ell get:

We\'ll substitute the sum of the first 9 terms of natural numbers by:

S9 = (1+9)*9/2

S=11(1+2+3+4+5+6+7+9)

S=11*(9*(1+9))/2

S = 11*9*5

S=495