Question

这道求极限怎么做

Answer 1

1/［(2k-1)(2k+1)］=1/2*［1/(2k-1)-1/(2k+1)］
∑(k=1到n) 1/［(2k-1)(2k+1)］
=1/2∑(k=1到n)［1/(2k-1)-1/(2k+1)］
=1/2*［1-1/(2k+1)］
=1/2-1/［2(2k+1)］
对上式求极限得，1/2

追答

1/［(2k-1)(2k+1)］=1/2*［1/(2k-1)-1/(2k+1)］
∑(k=1到n) 1/［(2k-1)(2k+1)］
=1/2∑(k=1到n)［1/(2k-1)-1/(2k+1)］
=1/2*［1-1/(2n+1)］
=1/2-1/［2(2n+1)］
对上式求极限得，1/2

Answer 2

=1/2（1-1/3+1/3-1/5+...+1/(2n-1)-1/(2n+1)
=1/2(1-1/(2n+1))
=1/2-1/(4n+2)
趋向于0当n趋于无穷时

Answer 3

裂项相消