Explicație pas cu pas:
progresie geometrică
[tex]S_{n} = \frac{b_{1}\cdot( {q}^{n} - 1)}{q - 1} \\ [/tex]
→
[tex]b = 7 + {7}^{2} + {7}^{3} + ... + {7}^{43} \\ [/tex]
[tex]b_{1} = 7, q = 7, n = 43[/tex]
[tex]\implies b = \frac{7\cdot( {7}^{43} - 1)}{7 - 1} = \frac{7\cdot( {7}^{43} - 1)}{6} \\ [/tex]
→
[tex]c = {3}^{0} + {3}^{1} + {3}^{2} + ... + {3}^{42} \\ [/tex]
[tex]b_{1} = 1, q = 3, n = 43[/tex]
[tex]\implies c = \frac{1\cdot( {3}^{43} - 1)}{3 - 1} = \frac{{3}^{43} - 1}{2} \\ [/tex]
→
[tex]d = 8 + {8}^{2} + {8}^{3} + ... + {8}^{88} \\ [/tex]
[tex]b_{1} = 8, q = 8, n = 88[/tex]
[tex]\implies d = \frac{8\cdot( {8}^{88} - 1)}{8 - 1} = \frac{8\cdot( {8}^{88} - 1)}{7} \\ [/tex]
