Category: Algebra

Question Number 164533 by alephzero last updated on 18/Jan/22 $$\mathrm{Prove},\mathrm{that}$$$$1)\underset{k=1}{\sum ^{\alpha }}\frac{1}{k(k+1)}=\frac{\alpha }{\alpha +1}$$$$2)\underset{x\to \mathrm{\infty }}{\lim }\underset{k=1}{\sum ^{\mathrm{\infty }}}\frac{1}{k(k+x)}=0$$ Answered by amin96 last…

Question Number 164511 by HongKing last updated on 18/Jan/22 $$\sin \cdot \left(\pi \sin \mathrm{x}\right)-\cos \cdot \left(\pi \sin \mathrm{x}\right)=1$$$$\mathrm{find}\mathbf{x}=?$$ Answered by mindispower last updated on 18/Jan/22 $$sin\left(a\right)-cos\left(a\right)=\sqrt{2}sin(a-\frac{\pi }{4})$$$$\Leftrightarrow\:{withea}=\pi{sin}\left({x}\right) \…

Question Number 164497 by mnjuly1970 last updated on 18/Jan/22 Answered by cortano1 last updated on 18/Jan/22 Commented by mnjuly1970 last updated on 18/Jan/22 $${thanks}\:{alot}\:{sir}\:{cortano} \…

Question Number 98925 by ajfour last updated on 17/Jun/20 $$Ifthecurveshownbelowhasthe$$$$equation,y=(x-p)(x^3-bx-c)$$$$thenfindq/pintermsofbandc.$$ Commented by ajfour last updated on 17/Jun/20 Answered…

Question Number 164451 by Zaynal last updated on 17/Jan/22 $$\mathbf{How}\mathbf{do}\mathbf{you}\mathbf{all}\mathbf{to}\mathbf{prove}\mathbf{is}\mathbf{true}\mathbf{or}\mathbf{false}??;$$$$$$$$\mathit{P}\mathit{r}\mathit{o}\mathit{v}\mathit{e}\mathit{t}\mathit{h}\mathit{e}:$$$$\:\frac{\mathrm{1}}{\mathrm{1}+\boldsymbol{\mathrm{p}}+\boldsymbol{\mathrm{p}}^{\mathrm{2}} +\boldsymbol{\mathrm{p}}^{\mathrm{3}} }\:+\:\frac{\mathrm{1}}{\mathrm{1}+\boldsymbol{{q}}+\boldsymbol{{q}}^{\mathrm{2}} +\boldsymbol{{q}}^{\mathrm{3}} }\:+\:\frac{\mathrm{1}}{\mathrm{1}+\boldsymbol{{r}}+\boldsymbol{{r}}^{\mathrm{2}} +\boldsymbol{{r}}^{\mathrm{3}} }\:+\:\frac{\mathrm{1}}{\mathrm{1}+\boldsymbol{{s}}+\boldsymbol{{s}}^{\mathrm{2}} +\boldsymbol{{s}}^{\mathrm{3}\:} }\:\geqslant\:\mathrm{1} \…