计算:1/2×4+1/4×6+1/6×8+……+1/(2n-4)(2n-2)+1/(2n-2).2n(n为正整数)

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计算:1/2×4+1/4×6+1/6×8+……+1/(2n-4)(2n-2)+1/(2n-2).2n(n为正整数)计算:1/2×4+1/4×6+1/6×8+……+1/(2n-4)(2n-2)+1/(2

计算:1/2×4+1/4×6+1/6×8+……+1/(2n-4)(2n-2)+1/(2n-2).2n(n为正整数)
计算:1/2×4+1/4×6+1/6×8+……+1/(2n-4)(2n-2)+1/(2n-2).2n(n为正整数)

计算:1/2×4+1/4×6+1/6×8+……+1/(2n-4)(2n-2)+1/(2n-2).2n(n为正整数)
原式
=1/2×(1/2-1/4+1/4-1/6+1/6-1/8+...+1/2n-4-1/2n-2)
=1/2×(1/2-1/2n-2)
=1/2×[1/2-1/2(n-1)]
=1/4×(1-1/n-1)
=n-2/4(n-1)

列项相消法

数学归纳法 妥妥的

=1/2(2/2×4+2/4×6+2/6×8+……+2/(2n-4)(2n-2)+2/(2n-2).2n)
=1/2(1/2-1/4+1/4-1/6+...+1/(2n-2)-1/2n)
=1/2(1/2-1/2n)
=1/4-1/4n
n>=3,n为整数