## Aryang 2 years ago a challenge question for all if 1035 + summation( tan( j pi/180) ) from j =0 to 45 = 2^x then x= 1) 20 2)21 3)22 4)23

1. zepdrix

I don't know the answer, but I thought I'd format this for you so it's a little easier to read. Hopefully I read it correctly.$\huge 1035+ \sum_{\color{royalblue}{j}=0}^{45}\; \tan\left(\color{royalblue}{j}\frac{\pi}{180}\right) \quad = \quad 2^x$ $\huge x= \;\color{green}{?}$

2. Compassionate

x = 22

3. Aryang

@Compassionate nopes..though you were close on the logic i guess.. @zepdrix yep,,thats the right interpretation..

4. mukushla

how can it be a power of 2 with ur options :) because$\large \sum_{\color{royalblue}{j}=0}^{45}\; \tan\left(\color{royalblue}{j}\frac{\pi}{180}\right) \quad <45 \ \tan \frac{\pi}{4}=45$if im not wrong

5. Aryang

please whosover sees it atleast bookmark it, so that if someone tells the solution or finally i tell the solution, you get to know that the solution really exists and is a genius one! :) note that i couldnt solve it either, but one of my professors did..

6. Aryang

not professors, teachers..

7. Zarkon

$N\left[1035+\sum _{j=0}^{45} \text{Tan}\left[j*\frac{\pi }{180}\right],20\right]$ Out[15]= 1055.3586583514306367

8. shubhamsrg

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9. Aryang

@mukushla yep that inequality is correct but how do you come to your conclusion ? as according to me,,the question is perfectly fine..

10. waterineyes

@mukushla has proved your question wrong with his Extra ordinary thinking.. ha ha ha...

11. Aryang

well i'd be glad if i am proved wrong..am waiting for him to reason this out..

12. waterineyes

He comes rarely online now a days ..

13. queelius

Uh, I got x=10.0435176596052.

14. waterineyes

So, it means the term : $$\large \sum_{\color{royalblue}{j}=0}^{45}\; \tan\left(\color{royalblue}{j}\frac{\pi}{180}\right)$$ can have one of the four values according to the choices given : 1047541 Or 2096117 Or 4193269 Or 8387573..

15. waterineyes

Something looks wrong to me..

16. waterineyes

Do you have given right choices there @Aryang

17. Aryang

now that all of you are saying it,,even am smelling something fishy here..i'll confirm and get back here asap..

18. waterineyes

It is better now to confirm it..

19. soty2013

is it an IIT question ?

20. shubhamsrg

well one thing i can easily make out is 1035 = summ( j) from j=0 to 45 so LHS on whole can be written as summation (j + tan(j pi/180) ) from j=0 to 45 my personal query is that, are you sure its summation there? if thats the product symbol there,,i can easily come to ans.otherwise i doubt,.,

21. bdh9800

I got$x \approx 10.04351766$

22. Callisto

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23. sauravshakya

as @mukushla said |dw:1356354261761:dw| and there is no number which can be expressed as 2^x where x is a integer between 1035 and 1080

24. robtobey

@bdh9800's numerical answer is correct. x = 10.0435176596051999738145449873985899460812855308 to 48 digits. Refer to the attached Mathematica solution.