Question

calculeaza suma tuturor nr. de forma :

a) aa; b) aaa; c) aaaa;

Answer 1

a) aa;
11, 22, 33, 44, 55, 66, 77, 88, 99

11+22+33+44+55+66+77+88+99=
495


b) aaa;

111, 222, 333, 444, 555, 666, 777, 888, 999

111+222+333+444+555+666+777+888+999=
4 995


c) aaaa;


1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999

1111+2222+3333+4444+5555+6666+7777+8888+9999=
49 995

Answer 2

a) aa

S = 11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99

S = 11 × ( 1 + 2 + 3 + 4 + ...... + 9 )

S = 11 × 9 × 10 : 2

S = 99 × 5

S = 495

sau:

S = ( 11 + 99 ) + ( 22 + 88 ) + ( 33 + 77 ) + ( 44 + 66 ) + 55

S = 110 × 4 + 55

S = 440 + 55

S = 495

__________________

b) aaa

S = 111 + 222 + 333 + 444 + ......... + 999

S = 111 × ( 1 + 2 + 3 + ..... + 9 )

S = 111 × 9 × 10 : 2

S = 9990 : 2

S = 4 995

_________________

c)   aaaa

S = 1111 + 2222 + 3333 +....... + 9 999

S = 1111 × ( 1 + 2 + 3 + ..... + 9 )

S = 1111 × 9 × 10 : 2

S = 99 990 : 2

S = 49 995