Question

Calculați suma : a)22+25+28+....301
b)32+39+46+...+753

c)43+51+59+...-1003
d)50+56+62+...+350
e)75+80+85+...+555

Answer 1

a) 22+25+28+........+301=

Suma Gauss =a+b+c+..n=(n+a)×[(n-a):(b-a)+1]:2

=(301+1)x(numarul de termeni):2
numarul de termeni=(301-22):3+1=279:3+1
=93+1
=94
22+25+28+.........+301=
=(301+1)x94:2
=302x94:2
=14194
22+25+28+........+301=14194
b)32+39+46+...+753
=(753+1)x(numarul de termeni):2
numarul de termeni=(753-32):7+1=
=721:7+1=103+1=104
32+39+46+...+753=(753+1)×104:2
=754×104:2
=40820

32+39+46+...+753=40820

c)43+51+59+...+1003
(1003+43)×[(1003-43):(51-43)+1]:2
=1046×[(960:8+1]:2
=1046×121:2
=63283
43+51+59+...+1003=63283

e)75+80+85+...+555
Suma Gauss =a+b+c+..n=(n+a)×[(n-a):(b-a)+1]:2
75+80+85+90+95+100....555
=(555+75)×[(555-75):5+1]:2
=630×97:2
=30555
75+80+85+...+555=30555


dupa acelasi model se fac toate punctele