Omega বিষয়ক
If 'ω\omegaω' is a complex cube root of unity,then ω(13+29+427...∞)+ω(12nbsp;+38+932...∞nbsp;)=\omega ^{ \begin{pmatrix} \frac { 1 }{ 3 }+\frac { 2 }{ 9 } +\frac { 4 }{ 27 } ...\infty \end{pmatrix} }+\omega^{ \begin{pmatrix} \frac { 1 }{ 2 } +\frac { 3 }{ 8 } +\frac { 9 }{ 32 } ...\infty \end{pmatrix} }=ω(31+92+274...∞)+ω(21nbsp;+83+329...∞nbsp;)=
111
−1-1−1
ω\omegaω
iii
13+29+427+......+∞\dfrac{1}{3}+\dfrac{2}{9}+\dfrac{4}{27}+......+\infty31+92+274+......+∞ (infinte G.P.)
Sω=a1−r=1S_\omega = \dfrac{a}{1-r} =1Sω=1−ra=1
12+38+932+......+∞\dfrac{1}{2}+\dfrac{3}{8}+\dfrac{9}{32}+......+\infty21+83+329+......+∞ (infinte G.P.)
Sω=a1−r=2S_\omega = \dfrac{a}{1-r} =2Sω=1−ra=2
We know,
1+ω+ω2=0∴ ω1+ω2=−1 1+\omega+\omega^2=0\\ \therefore\, \omega^1+\omega^2=-11+ω+ω2=0∴ω1+ω2=−1
x=−1+−32then,x101+x200=? x = \frac{- 1 + \sqrt{- 3}}{2} t h e n , x^{101} + x^{200} = ? x=2−1+−3then,x101+x200=?
x2 + x + 1=0 হলে x3 এর মান কত ?
ωn=ω হলে n কে 3 দ্বারা ভাগ করলে ভাগশেষ কত হবে?
এককের কাল্পনিক ঘনমূল ω \omega ω হলে, (1+ω)(1+ω4)(1+ω8)(1+ω12) \left ( 1 + \omega \right ) \left ( 1 + \omega^{4} \right ) \left ( 1 + \omega^{8} \right ) \left ( 1 + \omega^{12} \right ) (1+ω)(1+ω4)(1+ω8)(1+ω12) এর মান কত ?
