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advanced-calculus-prove-n-1-H-n-n-3-pi-4-72-note-H-n-1-1-2-1-n-




Question Number 123456 by mnjuly1970 last updated on 25/Nov/20
      ... advanced   calculus...                 prove::           φ=Σ_(n=1) ^∞ ( (H_n /n^3 ) )=^(???) (π^4 /(72))         note: H_n =1+(1/2)+...+(1/n)
$$\:\:\:\:\:\:…\:{advanced}\:\:\:{calculus}… \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{prove}:: \\ $$$$\:\:\:\:\:\:\:\:\:\phi=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\:\frac{\mathrm{H}_{{n}} }{{n}^{\mathrm{3}} }\:\right)\overset{???} {=}\frac{\pi^{\mathrm{4}} }{\mathrm{72}} \\ $$$$\:\:\:\:\:\:\:{note}:\:\mathrm{H}_{{n}} =\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+…+\frac{\mathrm{1}}{{n}} \\ $$

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