Question

根号下1+1/n^2+1/(n+1)^2的值是多少？

A.1+1/n+1/(n+1) B.1-1/n+1/(n+1) C.1+1/n-1/(n+1) D.1-1/n-1/(n+1)

请给我个详细过程，多谢了。

Answer 1

√[1+1/n²+1/(n+1)²]的值是多少？

选C。

解：
√[1+1/n²+1/(n+1)²]
=√[(n²+1)/n²+1/(n+1)²]
=√{[(n²+1)(n+1)²+n²]/[n²(n+1)²]}
=√{[(n²+1)(n+1)²+n²]}/n(n+1)
=√[(n²+1)(n²+2n+1)+n²]/n(n+1)
=√[(n²+1)(n²+1+2n)+n²]/n(n+1)
=√[(n²+1)²+2n(n²+1)+n²]/n(n+1)
=√[(n²+1+n)²]/n(n+1)
=(n²+1+n)/n(n+1)
=[n(n+1)+1]/n(n+1)
=1+1/n(n+1)
=1+1/n-1/(n+1)

Answer 2

没分的