WBJEE · Maths · Sequences and Series
If \(\omega\) is an imaginary cube root of unity, then the value of \((2-\omega)\left(2-\omega^{2}\right)+2(3-\omega)\left(3-\omega^{2}\right)\) \(+\ldots+(n-1)(n-\omega)\left(n-\omega^{2}\right)\) is
- A \(\frac{n^{2}}{4}(n+1)^{2}-n\)
- B \(\frac{n^{2}}{4}(n+1)^{2}+n\)
- C \(\frac{n^{2}}{4}(n+1)^{2}\)
- D \(\frac{n^{2}}{4}(n+1)-n\)
Answer & Solution
Correct Answer
(A) \(\frac{n^{2}}{4}(n+1)^{2}-n\)
Step-by-step Solution
Detailed explanation
Given, \((2-\omega)\left(2-\omega^{2}\right)+2(3-\omega)\left(3 \omega^{2}\right)+\ldots+\) \(\quad(n-1)(n-\omega)\left(n \omega^{2}\right)\) Now,…
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 \(z_{1}, z_{2}, z_{3}\) are imaginary numbers such that \(\left|z_{1}\right|=\left|z_{2}\right|=\left|z_{3}\right|=\left|\frac{1}{z_{1}}+\frac{1}{z_{2}}+\frac{1}{z_{3}}\right|=1,\) then
\(\left|z_{1}+z_{2}+z_{3}\right|\) isWBJEE 2016 Medium - Consider the function \(y=\log _{a}\left(x+\sqrt{\left.x^{2}+1\right)}\right.\) \(a>0, a \neq 1 .\) The inverse of the functionWBJEE 2018 Medium
- The cosine of the angle between any two diagonals of a cube isWBJEE 2016 Medium
- A point moves in such a way that the difference of its distance from two points (8,0) and (-8,0) always remains \(4 .\) Then, the locus of the point isWBJEE 2012 Easy
- Let \(f(x)=2 x^{2}+5 x+1\). If we write \(f(x)\) as \(f(x)=a(x+1)(x-2)+b(x-2)(x-1)+c(x-1)(x+1)\)
for real numbers \(a, b, c,\) thenWBJEE 2014 Hard - If \(f(x)=\left\{\begin{array}{ll}x^{3}-3 x+2, & x < 2 \\ x^{3}-6 x^{2}+9 x+2, & x \geq 2\end{array}\right.\) thenWBJEE 2013 Medium
More PYQs from WBJEE
- If \(x+\log _{10}\left(1+2^{x}\right)=x \log _{10} 5+\log _{10} 6,\) then
the value of \(x\) isWBJEE 2018 Medium - The function \(f: \mathbb{R} \rightarrow \mathbb{R}\) defined by \(f(x)=e^x+e^{-x}\) isWBJEE 2024 Easy
- A particle is moving in \(x-y\) plane according to \(\vec{r}=b \cos \omega t \hat{i}+b \sin \omega t \hat{j}\). Where \(\omega\) is constant. Which of the following statement(s) is / are true?WBJEE 2022 Medium
- The correct statement(s) about \(\mathrm{B}_2 \mathrm{H}_6\) is / are :WBJEE 2022 Easy
- Among the following, the one which is not a "green house gas", isWBJEE 2014 Easy
- The value of \(\int_{-100}^{100} \frac{\left(x+x^3+x^5\right)}{\left(1+x^2+x^4+x^6\right)} d x\) isWBJEE 2025 Easy