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**The Feynman Lectures on Physics, Spivak Calculus , Morrison and Boyd's Organic chemistry**and others. I took video lectures too from the internet like those of Sir Herbert Gross' , Leonard Susskind and some others. This site helped me a lot and is still helping me. So, due to all this I got indulged in Science and Maths the way our ancestors (early Mathematicians and Physicists) wanted us ( I apologize if I'm committing an offense by imagining just anything but due to etiquette I have used the plural form of first person instead of singular form, that is using 'us' instead of 'me').

The institutes in which I'm right now have something which I hate and I try to depict the reason of my hatred. Consider this problem from my book :-

Let $$ a_1 , a_2 , a_3 ....... $$ be an A.P. (Arithmetic Progression) . Prove that $$ \sum _{n=1} ^ {2m} (-1)^{n-1} a_n ^2 = \frac {m} {2m-1} ~ (a_1 ^2 - a_{2m} ^2) $$

Now, the problem is not that this question is hard or time consuming but to me it seems senseless. Let me give you some more taste of this

Evaluate :-

$$ sin (\pi/2) ~ sin (\pi/2^2) ~ sin (\pi/2^3)~~........ ~sin(\pi/2^{11}) ~ cos(\pi/2^{12})$$

My educators over there could solve these problems easily and every quickly. I'm sharing a link, please see it Calculus.

But I know and I believe that people here are far better, more experienced and more generous than these educators. So, I must state my problems explicitly and which is quite hard to do :-

*What is the difference between these problems and the problems we find in renowned books which are written by mathematicians?*Problems in renowned books are hard too ( like SL Loney's , Irodov's , G.H. Hardy's ) but they are quite different from these and my mind finds it pleasant to do those problems.

*Is there some problem with me only? Am I creating a non-existing dichotomy ? Are those question which I have stated not senseless?*

How should I survive ? They will conduct exams with these types of question?I know I can't leave things if I don't like them, I must have to adapt myself at least for sometime .

How should I survive ? They will conduct exams with these types of question?

I request all the senior members to please help me over here.

Thank you.