Đáp án:
Giải thích các bước giải:
b) `B=sin^2 2^{0}+sin^2 3^{0}+....+sin^2 88^{0}`
`B=(sin^2 2^{0}+sin^2 88^{0})+(sin^2 3^{0}+sin^2 87^{0})+....+(sin^2 44^{0}+sin^2 46^{0})+sin^2 45^{0}`
`B=(sin^2 2^{0}+cos^2 2^{0})+(sin^2 3^{0}+cos^2 3^{0})+....+(sin^2 44^{0}+cos^2 44^{0})+(\frac{\sqrt{2}}{2})^2`
`B=1+1+...+1+1/2` (có 43 số 1)
`B=87/2`
c) `\sqrt{2\sqrt{3\sqrt{4\sqrt{5....\sqrt{2016}}}} <3`
`=\sqrt{2\sqrt{3\sqrt{4\sqrt{5....\sqrt{2016}}}}} <\sqrt{2\sqrt{3...\sqrt{2015.2017}}}=\sqrt{2\sqrt{3...\sqrt{2014\sqrt{2016^2-1}}}}<\sqrt{2\sqrt{3...\sqrt{2014.2016}}}=\sqrt{2\sqrt{3\sqrt{2013\sqrt{2015^2-1}}}}=\sqrt{2\sqrt{3...\sqrt{2013.2015}}}<....<\sqrt{2.4}<3`
Vậy `⇒` đpcm
