Szereg

[matmabee]

Oblicz sumę szeregu
a)\( {4\over3} +1 + {3\over4} + {9\over16}+...\)
b) \(1- {1\over4} + {1\over16} - {1\over64} + ...\)
c) \(\sqrt{12}-\sqrt{6}+\sqrt{3}-\frac{\sqrt{6}}{2}+...\)

[eresh]

Oblicz sumę szeregu
a) 4/3 +1 + 3/4 + 9/16+...

\(a_1=\frac{4}{3}\\
q=\frac{3}{4}<1\\
S=\frac{\frac{4}{3}}{1-\frac{3}{4}}\\\)

[eresh]

Oblicz sumę szeregu

b) 1- 1/4 + 1/16 - 1/64 + ...

\(a_1=1\\
q=-\frac{1}{4}\\
|q|<1\\
S=\frac{1}{1+\frac{1}{4}}\)

[eresh]

Oblicz sumę szeregu

c) \(\sqrt{12}-\sqrt{6}+\sqrt{3}-\frac{\sqrt{6}}{2}+...\)

\(a_1=\sqrt{12}=2\sqrt{3}\\
q=-\frac{\sqrt{6}}{\sqrt{12}}=-\frac{1}{\sqrt{2}}=-\frac{\sqrt{2}}{2}\\
S=\frac{2\sqrt{3}}{1+\frac{\sqrt{2}}{2}}\\
S=\frac{4\sqrt{3}}{2+\sqrt{2}}
\)