证明1/2!+2/3!+3/4!+.+n/(n+1)!=1-1/(n+1)!
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![证明1/2!+2/3!+3/4!+.+n/(n+1)!=1-1/(n+1)!](/uploads/image/z/3860409-57-9.jpg?t=%E8%AF%81%E6%98%8E1%2F2%21%2B2%2F3%21%2B3%2F4%21%2B.%2Bn%2F%28n%2B1%29%21%3D1-1%2F%28n%2B1%29%21)
证明1/2!+2/3!+3/4!+.+n/(n+1)!=1-1/(n+1)!
证明1/2!+2/3!+3/4!+.+n/(n+1)!=1-1/(n+1)!
证明1/2!+2/3!+3/4!+.+n/(n+1)!=1-1/(n+1)!
n/(n+1)!
=[(n+1)-1]/(n+1)!
=(n+1)/(n+1)!-1/(n+1)!
=1/n!-1/(n+1)!
所以左边=1/1!-1/2!+1/2!-1/3!+……+1/n!-1/(n+1)!
=1-1/(n+1)!
n/(n+1)!=1/n!-1/(n+1)!
每个式子这样分解,加起来就行了