极限的符号不好打,省略了
第三题你会了,就不写了
1.根号(n^2+3n)-根号(n^2+1)
先化简得到（3-1/n）/[根号下(1+3/n)+根号下(1+1/n^2)]
当n趋向无穷时1/n,3/n,1/n^2都趋向于0,所以原式=3/2.
2.1+ (2^2+3^2)/5^2 + (2^3+3^3)/5^3 +……+(2^n+3^n)/5^n
=(2+3)/5+ (2^2+3^2)/5^2 + (2^3+3^3)/5^3 +……+(2^n+3^n)/5^n
=[2/5+(2/5)^2+(2/5)^3+…++(2/5)^n]+[3/5+(3/5)^2+(3/5)^3+…+(3/5)^n]
=(2/5)/[1-(2/5)]+(3/5)/[1-(3/5)]
=2/3+3/2
=13/6