Question

7) Calculati:
a) 1+2+3+4+...+100
b) 5+10 +15+20 +...+1000 x) 1+3+5+7+...+2003+2005.
c)1+3+5+7+...+2003+2005
ajutor urgent​

Answer 1

Explicație pas cu pas:

$\boxed {1 + 2 + 3 + ... + n = \dfrac{n \cdot (n + 1)}{2}}$

$\boxed{ 1 + 3+ 5 + ... + (2n - 1) = {n}^{2}}$

a)

$1 + 2 + 3 + ... + 100 = \dfrac{100 \cdot (100 + 1)}{2} = \dfrac{100 \cdot 101}{2} = \bf 5050$

b)

$5 + 10 + 15 + ... + 1000 = \\ = 5 \cdot (1 + 2 + 3 + ... + 200) \\ = 5 \cdot \dfrac{200 \cdot (200 + 1)}{2} \\ = \bf 5 \cdot 100 \cdot 201 = \bf 100500$

c)

$1 + 3 + 5 + ... + 2005 = 1 + 3 + 5 + ... + (2 \cdot 1003 - 1) = \bf {1003}^{2}$