Question

sa se calculeze suma cifrelor impare de doua cifre

Answer 1

Sa se calculeze suma numerelor impare de doua cifre :

11 + 13 + 15 +...+ 95 + 97 + 99 =
Aflam cati termeni are suma:
(99 - 11) : 2 + 1 = 88 : 2 + 1 = 45

= (11 + 99) × 45 : 2 =

= 110 × 45 : 2 =

= 55 × 45 =

= 2 475 (suma )

Answer 2

$11+13+15+...+99 = \\ \\ = (\bold1\cdot 2+9)+(\bold2\cdot2+9) +(\bold3 \cdot 2+9) +...+(\bold{45}\cdot 2+9) = \\ \\ =2\cdot (1+2+3+...+45) + 9\cdot 45 = \\ \\ = 2\cdot \dfrac{45\cdot(45+1)}{2} +(9+9+\underset{\text{de 45 ori}}{\underbrace{...}}+9)= \\ \\ = 45\cdot 46+9\cdot 45 = \\ \\ = 45\cdot(46+9) =\\ \\ = 45\cdot 55 = \\ \\ = 2475$