AP EAMCET · Maths · Complex Number
If \(1, a, a^2, \ldots, a^{n-1}\) are the \(n\)th roots of unity. Then \(\sum_{i=1}^{n-1} \frac{1}{2-a^i}\) is equal to
- A \((n-2) 2^n\)
- B \(\frac{(n-2) 2^{n-1}+1}{2^n-1}\)
- C \(\frac{(n-2) 2^{n-1}}{2^n-1}\)
- D \(\frac{1}{(n-2) 2^n}\)
Answer & Solution
Correct Answer
(B) \(\frac{(n-2) 2^{n-1}+1}{2^n-1}\)
Step-by-step Solution
Detailed explanation
\(\sum_{i=1}^{n-1} \frac{1}{2-\alpha^i}\) \(1, \alpha, \alpha^2, \ldots \ldots, \alpha^{n-1}\) are the \(n\)th root of unity…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If \(O\) is the origin and \(P, Q\) are points on the line \(3 x+4 y+\) \(15=0\) such that \(\mathrm{OP}=\mathrm{OQ}=9\), then the area of \(\triangle \mathrm{OPQ}\) isAP EAMCET 2023 Easy
- For the curve \(y=5 x-2 x^3\), if \(x\) increases at the rate of 2 units/sec, the rate of change in the slope of the curve at \(x=3\) is ......../secAP EAMCET 2021 Easy
- \(\int_0^\pi\left(\sin ^5 x \cos ^3 x+\sin ^4 x \cos ^4 x+\sin ^3 x \cos ^4 x\right) d x=\)AP EAMCET 2025 Medium
- \(\int \tan ^{-1}\left(\sqrt{\frac{1-x}{1+x}}\right) d x\) is equal toAP EAMCET 2007 Hard
- \(\int \frac{x^3-1}{x^3+x} d x=\)AP EAMCET 2020 Medium
- If and , where does not lie in the third quadrant, then is equal toAP EAMCET 2021 Easy
More PYQs from AP EAMCET
- The distance between the lines represented by \(x^2+2 x y+y^2-8 m x-8 m y-9 m^2=0\) isAP EAMCET 2017 Hard
- The domain of the real valued function
\(f(x)=\sqrt{\frac{2-|x|}{3-|x|}}\) isAP EAMCET 2022 Medium - If \(a_k\) is the coefficient of \(x^k\) in the expansion of
\(\left(1+x+x^2\right)^n\) for \(k=0,1,2, \ldots, 2 n\), then \(a_1+2 a_2+3 a_3+\ldots+2 n a_{2 n}\) is equal toAP EAMCET 2007 Medium - A radioactive decay forms an isotope of the original nucleus with the emission of the following particlesAP EAMCET 2023 Easy
- A square frame of side \(1 \mathrm{~m}\) carrying a current \(I\) produces a magnetic field \(B\) at its centre. The same current is passed through a circular coil having the same perimeter as the square. The magnetic field at the centre of the circular coil is \(B^{\prime}\). The ratio of \(\frac{B}{B^{\prime}}\) isAP EAMCET 2021 Medium
- If the pair of lines \(a x^2-7 x y-3 y^2=0\) and \(2 x^2+x y-6 y^2=0\) have exactly one line in common and ' \(a\) ' is an integer, then the equation of the pair of bisectors of the angles between the lines \(a x^2-7 x y-3 y^2=0\) isAP EAMCET 2025 Hard