Question

Va rog 19
Dau coroanaaa

Answer 1

a) 122

b)142

c)9,696

d)2,473

Answer 2

Explicație pas cu pas:

a) sumă are 34 termeni

$1 + 4 + 7 + 10 + ... + 100 = 1 + (1 + 3) + (1 + 6) + (1 + 9) + ... + (1 + 99) = \underbrace{1 + 1 + ... + 1}_{34} + (3 + 6 + 9 + ... + 99) = 34 + 3 \cdot (1 + 2 + 3 + ... + 33) = 34 + 3 \cdot \dfrac{33 \cdot 34}{2} = 34 + 1683 = \bf 1717$

sau:

$\dfrac{(1 + 100) \cdot 34}{2} = \dfrac{101 \cdot 34}{2} = \bf 1717$

b) suma are 17 termeni:

$2 + 8 + 14 + 20 + ... + 98 = 2 \cdot (1 + 4 + 7 + 10 + ... + 49) = 2 \cdot \dfrac{(1 + 49) \cdot 17}{2} = 50 \cdot 17 = \bf 850$

c) suma are 101 termeni:

$1918 + 1919 + 1920 + 1921 + ... + 2018 = \dfrac{(1918 + 2018) \cdot 101}{2} = \dfrac{3936 \cdot 101}{2} = \bf 198768$

d) suma are 954 termeni:

$111 + 113 + 115 + 117 + ... + 2017 = \dfrac{(111 + 2017) \cdot 954}{2} = \dfrac{2128 \cdot 954}{2} = \bf 1015056$