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Find-the-value-of-n-0-2020-2-n-1-3-2-n-




Question Number 109746 by Joel574 last updated on 25/Aug/20
Find the value of  Σ_(n = 0) ^(2020)  [(2^n /(1 + 3^((2^n )) ))]
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\underset{{n}\:=\:\mathrm{0}} {\overset{\mathrm{2020}} {\sum}}\:\left[\frac{\mathrm{2}^{{n}} }{\mathrm{1}\:+\:\mathrm{3}^{\left(\mathrm{2}^{{n}} \right)} }\right] \\ $$
Commented by Her_Majesty last updated on 25/Aug/20
≈.25
$$\approx.\mathrm{25} \\ $$
Commented by Joel574 last updated on 25/Aug/20
How?
$$\mathrm{How}? \\ $$
Commented by Her_Majesty last updated on 25/Aug/20
sorry, I misread 1≤n instead of 0≤n  it′s ≈.5
$${sorry},\:{I}\:{misread}\:\mathrm{1}\leqslant{n}\:{instead}\:{of}\:\mathrm{0}\leqslant{n} \\ $$$${it}'{s}\:\approx.\mathrm{5} \\ $$

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