Please Help

Please find the sum of series$\frac { 1 }{ 1 } +\frac { 1 }{ 4 } \frac { 1 }{ 64 } +............................................till \infty $. Post solutions too

#Series

Easy Math Editor

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

What's the next term in the series ?

I have a few options .

If it is $\dfrac{1}{3^{2}}\dfrac{1}{3^{3}}$

Then the series is $\zeta(5)$ . Look up Reimann Zeta function ,(sorry , I'm out of time so I can't provide u a link )

If it is $\dfrac{1}{3^{2}}\dfrac{1}{{2.3}^{2}}$

Then it will be $\dfrac{1}{4}\zeta(4)$ .

Have I satisfactorily answered ur doubt . I gotta dash . I have mentioned a few of my friends , they'll surely help u out :D

A Former Brilliant Member - 6 years, 2 months ago

@Kartik Sharma , @Ishan Dasgupta Samarendra , @Krishna Ar , @Sharky Kesa $\dots$

Am I correct ?

A Former Brilliant Member - 6 years, 2 months ago

Not sure, trying it now. @Kandarp Singh Look this up - it might help.

@Azhaghu Roopesh M See, this is one of the reasons I said you are the best person I know here. You always, always help others! @Pranjal Jain @Pratik Shastri @Samarpit Swain @Sandeep Bhardwaj Sir

User 123 - 6 years, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$