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Question Number 92976 by frc2crc last updated on 10/May/20

define  Δ_n =((n(1+n))/2)  find a closer form for  Σ_(n=1) ^∞ (1/Δ_n ^m )

$${define} \\ $$$$\Delta_{{n}} =\frac{{n}\left(\mathrm{1}+{n}\right)}{\mathrm{2}} \\ $$$${find}\:{a}\:{closer}\:{form}\:{for} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\Delta_{{n}} ^{{m}} } \\ $$

Answered by john santu last updated on 10/May/20

what Δ_n ^m  ?

$$\mathrm{what}\:\Delta_{\mathrm{n}} ^{\mathrm{m}} \:?\: \\ $$

Commented by frc2crc last updated on 10/May/20

Δ_n =((n^2 +n)/2)⇛Δ_n ^m =(((n^2 +n)^m )/2^m )

$$\Delta_{{n}} =\frac{{n}^{\mathrm{2}} +{n}}{\mathrm{2}}\Rrightarrow\Delta_{{n}} ^{{m}} =\frac{\left({n}^{\mathrm{2}} +{n}\right)^{{m}} }{\mathrm{2}^{{m}} } \\ $$

Commented by frc2crc last updated on 10/May/20

i used this definition

$${i}\:{used}\:{this}\:{definition} \\ $$

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