Question and Answers Forum

All Questions      Topic List

Geometry Questions

Previous in All Question      Next in All Question      

Previous in Geometry      Next in Geometry      

Question Number 189761 by normans last updated on 21/Mar/23

(x/(1×2)) + (x/(2×3)) + (x/(3×4)) + ......+ (x/(1998×1999)) + (x/(1999×2000)) = 1 x = ????

$$ \\ $$$$\:\:\frac{\boldsymbol{{x}}}{\mathrm{1}×\mathrm{2}}\:+\:\frac{\boldsymbol{{x}}}{\mathrm{2}×\mathrm{3}}\:+\:\frac{\boldsymbol{{x}}}{\mathrm{3}×\mathrm{4}}\:+\:......+\:\frac{\boldsymbol{{x}}}{\mathrm{1998}×\mathrm{1999}}\:+\:\frac{\boldsymbol{{x}}}{\mathrm{1999}×\mathrm{2000}}\:=\:\mathrm{1}\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{x}}\:=\:???? \\ $$$$ \\ $$

Answered by Frix last updated on 21/Mar/23

Σ_(k=1) ^n (x/(k(k+1))) =((xn)/(n+1))=1 ⇒ x=((n+1)/n)

$$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{{x}}{{k}\left({k}+\mathrm{1}\right)}\:=\frac{{xn}}{{n}+\mathrm{1}}=\mathrm{1}\:\Rightarrow\:{x}=\frac{{n}+\mathrm{1}}{{n}} \\ $$

Answered by BaliramKumar last updated on 21/Mar/23

x[(1/1) − (1/(2000))] = 1 x[((2000−1)/(2000))] = 1 x = ((2000)/(1999))

$${x}\left[\frac{\mathrm{1}}{\mathrm{1}}\:−\:\frac{\mathrm{1}}{\mathrm{2000}}\right]\:=\:\mathrm{1} \\ $$$${x}\left[\frac{\mathrm{2000}−\mathrm{1}}{\mathrm{2000}}\right]\:=\:\mathrm{1} \\ $$$${x}\:=\:\frac{\mathrm{2000}}{\mathrm{1999}} \\ $$

Answered by manxsol last updated on 21/Mar/23

x(1−(1/2)+(1/2)−(1/3)+.....(1/(1999))−(1/(2000)))=1 x(1−(1/(2000)))=1 x=((2000)/(1999))

$${x}\left(\mathrm{1}−\cancel{\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{3}}+.....\frac{\mathrm{1}}{\mathrm{1999}}}−\frac{\mathrm{1}}{\mathrm{2000}}\right)=\mathrm{1} \\ $$$${x}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2000}}\right)=\mathrm{1} \\ $$$${x}=\frac{\mathrm{2000}}{\mathrm{1999}} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com