这道题怎么做啊!求大神!!!过程!(最好拍照)
1个回答
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(1)原式=√[n²(n+1)²+(n+1)²+n²]/n(n+1)
=√{n²[(n+1)²+1]+(n+1)²}/n(n+1)
=√n²[n²+2(n+1)]+(n+1)²/n(n+1)
=√(n²)²+2n²(n+1)+(n+1)²/n(n+1)
=√(n²+n+1)²/n(n+1)
=(n²+n+1)/n(n+1)
=[(n+1)²-n]/n(n+1)
=1+1/n-1/(n+1)
(2)原式=1+1-1/2+1+1/2-1/3+……+1+1/n-1/(n+1)
当n=2014时
原式=2015 -1/2015
=√{n²[(n+1)²+1]+(n+1)²}/n(n+1)
=√n²[n²+2(n+1)]+(n+1)²/n(n+1)
=√(n²)²+2n²(n+1)+(n+1)²/n(n+1)
=√(n²+n+1)²/n(n+1)
=(n²+n+1)/n(n+1)
=[(n+1)²-n]/n(n+1)
=1+1/n-1/(n+1)
(2)原式=1+1-1/2+1+1/2-1/3+……+1+1/n-1/(n+1)
当n=2014时
原式=2015 -1/2015
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