Question

Calculati:

Dau coroana​

Answer 1

Răspuns:

i)1

j)10/n

k)9a/b

l)1

m)2

n) n

Explicație pas cu pas:

i)1/55+2/55+3/55+...+10/55=

*rezolvam suma lui Gauss de la numarator

1+2+3+...+10=(1+10)*10:2=11*5=55

1/55+2/55+3/55+...+10/55=55/55=1

j)2/n+3/n+5/n=10/n

k)a/b+3a/b+5a/b=9a/b

l)x/x+1+1/x+1=x+1/x+1=1

m)y+1/y+3+3/y+3+y+2/y+3=2y+6/y+3=2

n) 2/n+1+4/n+1+6/n+1+....+2n/n+1

*rezolvam suma lui Gauss de la numarator

2+4+6+...+2n=2(1+2+3+...+n)=2(1+n)*n:2=(n+1)*n

2/n+1+4/n+1+6/n+1+....+2n/n+1=n+1*n/n+1=n