just help me to do this

[clear whale]

(3x)½-(3x)¼-(3x)⅛-... = 5
Can i solve this question by this way ?
(3x-5)½=5
3x-5=25
3x=30
x=10

Can you solve this question by using SInfinity=a/(1-r)?
If u can then how

[clear whale]

<@&286206848099549185>

Sorry the original question is
[3x-(3x-(3x)½)½-...]½=5

[languid jungle]

Do you mean $\sqrt{3x -\sqrt{3x -\sqrt{3x -\sqrt{3x -...}}}}=5$?

[plucky prism]

Jay

[languid jungle]

If so, let $\text{LHS} = U \implies U = \sqrt{3x - U}$

the solve for $U$, then put $U=5$ and solve for $x$.

[plucky prism]

Jay

[languid jungle]

\begin{align*} U &= \sqrt{3x - U} \ U^2 &= 3x - U \ \text{But, $U=5$:} \quad 5^2 &= 3x - 5 \ 30 &= 3x \ x &= 10 \end{align*}

[plucky prism]

Jay

[languid jungle]

Expanding on the method I mentioned, @clear whale, and correcting the small error above.

[clear whale]

But can we solve this question via sequences formula ?

[languid jungle]

Not by using $S_{\infty} = \frac{a}{1-r}$ (as you aksed initially)

as that would require a GP, which we don't have.

You could form a sequence $u_1=\sqrt{3x-5}$

$u_2=\sqrt{3x-\sqrt{3x-5}}$

$u_3=\sqrt{3x-\sqrt{3x-\sqrt{3x-5}}}$

$u_n=\sqrt{3x-u_{n-1}}$

but this would only approach the same limiting value, as

the actual statement given is not actually a term of this sequence...

and, in any case, as this sequence is neither arithmetic nor geometric,

we don't have easy tools to use to explore its values.

[plucky prism]

Jay

[clear whale]

.close