Question

VA ROG URGENT

calculați următoarele sume:
a 2+2+4+...+50;
d 1+2+3+...124;
g 5+6+7+...81;
b 1+2+3+...+500;
e 2+4+6+...+600;
h 1+2+3+...+512;
c 1+97+2+999+3+198;
f 15+16+17+...+70
i 317+318+319+...+400​

DAU COROANA

Answer 1

Răspuns:

Bună, sper ca te am ajutat și cu atât!!

Answer 2

Explicație pas cu pas:

a)

$2+3+4+...+50 = (1 + 2+3+4+...+50) - 1 = \dfrac{50 \cdot (50 + 1)}{2} - 1 = \dfrac{50 \cdot 51}{2} - 1 = 1275 - 1 = \bf 1274$

b)

$1+2+3+...+500 = \dfrac{500 \cdot (500 + 1)}{2} = \dfrac{500 \cdot 501}{2} = \bf 125250$

c)

$1+97+2+999+3+198 = (1 + 999) + (2 + 198) + (3 + 97) = 1000 + 200 + 100 = \bf 1300$

d)

$1+2+3+...+124 = \dfrac{124 \cdot (124 + 1)}{2} = \dfrac{124 \cdot 125}{2} = \bf 7750$

e)

$2 + 4 + 6 + ... + 600 = 2 \cdot (1 + 2 + 3 + ... + 300) = 2 \cdot \dfrac{300 \cdot (300 + 1)}{2} = 2 \cdot \dfrac{300 \cdot 301}{2} = 300 \cdot 301 = \bf 90300$

f)

$15 + 16 + 17 + ... + 70 = (1 + 2 + 3 + ... + 70) - (1 + 2 + 3 + ... + 14) = \dfrac{70 \cdot (70 + 1)}{2} - \dfrac{14 \cdot (14 + 1)}{2} = \dfrac{70 \cdot 71}{2} - \dfrac{14 \cdot 15}{2} = 2485 - 105 = \bf 2380$

g)

$5 + 6 + 7 + ... + 81 = (1 + 2 + 3 + ... + 81) - (1 + 2 + 3 + 4) = \dfrac{81 \cdot (81 + 1)}{2} - 10 = \dfrac{81 \cdot 82}{2} - 10 = 3321 - 10 = \bf 3311$

h) 1+2+3+...+512

$1 + 2 + 3 + ... + 512 = \dfrac{512 \cdot (512 + 1)}{2} = \dfrac{512 \cdot 513}{2} = \bf 131328$

i)

$317 + 318 + 319 + ... + 400 = (1 + 2 + 3 + ... + 400) - (1 + 2 + 3 + ... + 316) = \dfrac{400 \cdot (400 + 1)}{2} - \dfrac{316 \cdot (316 + 1)}{2} = \dfrac{400 \cdot 401}{2} - \dfrac{316 \cdot 317}{2} = 80200 - 50086 = \bf 30114$