数列1⼀(1*4),1⼀(4*7),1⼀(7*10),···,1⼀[(3n-2)*(3n+1)]的前

2025-04-17 23:29:45
推荐回答(2个)
回答1:

(3n-2)×(3n+1)分之一
=1/3*[1/(3n+1)-1/(3n-2)]
1×4分之1+4×7分之1+···+(3n-2)×(3n+1)分之1
=1/3*[1/4-1+1/7-1/4+1/10-1/7+...+1/(3n+1)-1/(3n-2)]
=1/3*[-1+1/(3n+1)]
=1/3(3n+1)-1/3

回答2:

1×4分之1+4×7分之1+···+(3n-2)×(3n+1)分之1=1/3*(1-1/4+1/4-1/7+……+1/(3n+1))=1/3(1-1/(3n+1))