Question

* S₁ =6+12+18+...........+180
Prin metoda lui Gauss!Vă rog repede!​

Answer 1

$6 + 12 + 18 + ... + 180 \\ = 6(\underbrace{1 + 2 + 3 + ... + 30} _{30 \: \: \: termeni} ) \\ \\ =\not 6\cdot \frac{30\cdot(30 + 1)}{\not2} \\ \\ = 3\cdot30\cdot31 \\ = 90 \cdot31 \\ = 2790 \\ \\ \\ \\ \\ \\ \\ \\ \underline{formula \: \: \: lui \: \: gauss }: \\ \underbrace{1 + 2 + 3 + ... + n} _{n \: \: \: termeni} = \\ \\ nr . \: \: \: termeni \cdot(ultimul \: \: \: termen + 1)\over2 \\ \\ = \boxed{ \frac{n\cdot(n + 1)}{2} }$

Answer 2

Răspuns:

6+12+18+...+180

=6(

30termeni

1+2+3+...+30

)

=



6⋅



2

30⋅(30+1)

=3⋅30⋅31

=90⋅31

=2790

formulaluigauss

:

ntermeni

1+2+3+...+n

=

2

nr.termeni⋅(ultimultermen+1)

=

2

n⋅(n+1)