Question

b=7+7²+7³+...+7⁴³
c=3⁰+3¹+3²+3³+...+3⁴²
d=8+8²+8³+...+8⁸⁸
ajutor:^​

Answer 1

Explicație pas cu pas:

progresie geometrică

$S_{n} = \frac{b_{1}\cdot( {q}^{n} - 1)}{q - 1}$

→

$b = 7 + {7}^{2} + {7}^{3} + ... + {7}^{43}$

$b_{1} = 7, q = 7, n = 43$

$\implies b = \frac{7\cdot( {7}^{43} - 1)}{7 - 1} = \frac{7\cdot( {7}^{43} - 1)}{6}$

→

$c = {3}^{0} + {3}^{1} + {3}^{2} + ... + {3}^{42}$

$b_{1} = 1, q = 3, n = 43$

$\implies c = \frac{1\cdot( {3}^{43} - 1)}{3 - 1} = \frac{{3}^{43} - 1}{2}$

→

$d = 8 + {8}^{2} + {8}^{3} + ... + {8}^{88}$

$b_{1} = 8, q = 8, n = 88$

$\implies d = \frac{8\cdot( {8}^{88} - 1)}{8 - 1} = \frac{8\cdot( {8}^{88} - 1)}{7}$