`bb(b o t)`

`bb(1.)`

`E =1/(sqrt1 +sqrt2) +1/(sqrt2 +sqrt3) + .... +1/(sqrt2014 +sqrt2015)`

Ta có `:`

`1/(sqrta + sqrt{a+1}) = (sqrt{a+1} -sqrta)/((sqrta+sqrt{a+1})(sqrt{a+1} -sqrta)) `

`= (sqrt{a+1} -sqrta)/((a+1) -a) = (sqrt{a+1} -sqrta)/1 = sqrt{a+1} -sqrta`

Khi đó `:`

`E = sqrt2 - sqrt1 + sqrt3 - sqrt1 + .... +sqrt2015 - sqrt2014`

`E = sqrt2015 - sqrt1`

`E = sqrt2015 - 1`

`bb(2.)`

`A = 1/(1sqrt2 + 2sqrt1) +1/(2sqrt3 +3sqrt2) + .... +1/(2014sqrt2015 +2015sqrt2014)`

Ta có `:`

`1/(asqrt{a+1} + (a+1)sqrta)`

`= 1/(sqrt{a.(a+1)} . (sqrta + sqrt{a+1}))`

`= (sqrt{a+1} - sqrta)/(sqrt{a(a+1)} .(sqrt{a+1} +sqrta)(sqrt{a+1} -sqrta))`

`=(sqrt{a+1)-sqrta)/(sqrt{a(a+1)} . (a+1-a))`

`=(sqrt{a+1} -sqrta)/(sqrt{a(a+1))`

`=1/sqrta - 1/(sqrt{a+1})`

Khi đó `:`

`A = 1/sqrt1 - 1/sqrt2 + 1/sqrt2 -1/sqrt3 + .... +1/sqrt2014 - 1/sqrt2015`

`A = 1/1 - 1/sqrt2015`

`A = 1 - sqrt2015/2015`

`A=(2015 - sqrt2015)/2015 .`