Question

simplifica fractia 2+5+8+....+362/3+7+11+....+483

Answer 1

2+5+8+....+362/3+7+11+....+483
raport de 2 progresii aritmetice

2+5+8+....+362
a1=2, an=362,  r= 3 (cresc din 3 in 3)
, an=a1+(n-1)×r
362=2+(n-1)×3
362=2+3n-3
362+1=3n
363=3n
n=121
S₁= [(a1+an)/2]×n
S₁=[(2+362)/2]×121=182×121=22022


3+7+11+....+483
a1=3, an=483,  r= 4 (cresc din 4 in 4)
, an=a1+(n-1)×r
483=3+(n-1)×4
483=3+4n-4
484=4n
n=121
S₂= [(a1+an)/2]×n
S₂=[(3+483)/2]×121=243×121=29403

S=S₁:S₂=(182×121):(243×121)

S = 182/243