Question 60

When expressed in a decimal form, which of the following numbers will be non - terminating as well as non-repeating?

Solution

Option A: $$\left(\frac{\pi}{2}\right) \left[\left(\frac{1}{\pi}\right) + 1\right] - \frac{\pi}{2}$$ =1/2

Option B: $$\sin^2 1^\circ + \sin^2 2^\circ + .... + \sin^2 {89}^\circ$$ =44+1/2 ($$\sin^2\left(89\right)=\cos^2\left(1\right)\ \&\ \sin^2\left(1\right)+\cos^2\left(1\right)=1$$

Option C: $$\sqrt{2}\left(3\sqrt{2} - \frac{4}{\sqrt{2}}\right) + \sqrt{3}$$ = $$6-4+\sqrt{3}$$=$$2+\sqrt{3}$$ which is non-terminating and non repeating.

Option D: $$\frac{\left(\sqrt[3]{729}\right)}{3} + \frac{22}{7}$$ =3+22/7

Option E: $$\left(\frac{\pi}{4}\right) + \left(\frac{\pi}{4}\right)^2 + \left(\frac{\pi}{4}\right)^3 + ...$$ (infinite terms)= $$\frac{1}{1-\frac{\pi\ }{4}}=\frac{4}{4\ -\pi\ }\ $$ => $$(4 - \pi)[1 + \left(\frac{\pi}{4}\right) + \left(\frac{\pi}{4}\right)^2 + \left(\frac{\pi}{4}\right)^3 + ...$$ (infinite terms)] =4


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