(1)计算:+2*2!+3*3!+……+n*n!(2)求证:k/(k+1)!=1/k!-1/(k+1)!(3)求证:1/
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(1)计算:+2*2!+3*3!+……+n*n!(2)求证:k/(k+1)!=1/k!-1/(k+1)!(3)求证:1/2!+2/3!+n/(n+1)!...
(1)计算:+2*2!+3*3!+……+n*n!
(2)求证:k/(k+1)!=1/k!-1/(k+1)!
(3)求证:1/2!+2/3!+n/(n+1)!=1-1/(n+1)
(1)计算:+2*2!+3*3!+……+n*n!
(2)求证:k/(k+1)!=1/k!-1/(k+1)!
(3)求证:1/2!+2/3!+n/(n+1)!=1-1/(n+1)
(1)
ak=k*k!=(k+1-1)k!=(k+1)!-k!
1!+2*2!+3*3!+...+n*n!
=1!+3!-2!+4!-3!+...+(n+1)!-n!
=(n+1)!-1
(2)
1/k!-1/(k+1)!=1/k!-1/[(k+1)k!]
=(1/k!)[1-1/(k+1)]
=k/(k+1)!(3)限制长度了,提示用第二问结论.
ak=k*k!=(k+1-1)k!=(k+1)!-k!
1!+2*2!+3*3!+...+n*n!
=1!+3!-2!+4!-3!+...+(n+1)!-n!
=(n+1)!-1
(2)
1/k!-1/(k+1)!=1/k!-1/[(k+1)k!]
=(1/k!)[1-1/(k+1)]
=k/(k+1)!(3)限制长度了,提示用第二问结论.
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