PLEASE AIDEZ MOI Calculer chacune des sommes suivantes : a. S = 13+13^2+13^3...+13^19. b. S = 1+5+25+125...+ 15625 c. S = 1+1/2+1/4+1/8...+1/1024 Pourriez-vous

Bonjour,

a)

[tex]13+13^2+13^3+...+13^{19}=1+13+13^2+13^3+...+13^[19}-1\\\\=\dfrac{13^{20}-1}{13-1}-1 \\\\=\dfrac{19004963774880799438801-1}{12}-1 \\\\=1583746981240066619899\\[/tex]

b)

[tex]1+5+5^2+5^3+...+5^6=\dfrac{5^7-1}{5-1} \\\\=\dfrac{78125-1}{4} \\\\=19531\\[/tex]

c)

[tex]1+\dfrac{1}{2} +\dfrac{1}{4} +\dfrac{1}{8} +...+\dfrac{1}{1024} \\\\=1+\dfrac{1}{2} +(\dfrac{1}{2}) ^2+(\dfrac{1}{2} )^3+...+(\dfrac{1}{2} )^{10}\\\\\dfrac{(\dfrac{1}{2})^{11}-1 }{\dfrac{1}{2} -1} \\\\\dfrac{\dfrac{1}{2048}-1}{-\dfrac{1}{2} } \\\\=\dfrac{2047}{1024} \\[/tex]