Menu Close

x-1-2-x-2-3-x-3-4-x-1998-1999-x-1999-2000-1-x-

Tinku Tara 0 Comments
Pin




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

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *