利用因式分解计算:(1-1⼀2눀)(1-1⼀3눀)(1-1⼀4눀)···(1-⼀n눀)

2024-11-08 09:33:24
推荐回答(2个)
回答(1):

:(1-1/2²)(1-1/3²)(1-1/4²)···(1-/n²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)·····(1-1/n)(1+1/n)
=1/2×3/2×2/3×4/3×3/4×5/4×···×(n-1)/n×(n+1)/n
=1/2×(n+1)/n
=(n+1)/(2n)

回答(2):

:(1-1/2²)(1-1/3²)(1-1/4²)···(1-/n²)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/n)(1+1/n)
=1/2×(n+1)/n
=(n+1)/(2n)