Question

b) = 7+7^2+7^3+...+7^43
c) c = 3° +3¹ +3² +3³ + + 342; d d=8+8² +8³ + ... + 888. c c = 3 ° + 3¹ + 3² + 3³ + + 342 ;
d) d = 8 + 8² + 8³ + ... + 888 .


Va rogggg.Urgentt.Dau coroana(cand imi v-a aparea)​

Answer 1

Răspuns:

progresie geometrică

Explicație:

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

b)

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

$b = 7 + {7}^{2} + {7}^{3} + ... + {7}^{43} = \\ = \frac{7\cdot ( {7}^{43} - 1)}{7 - 1} = \frac{7\cdot ( {7}^{43} - 1)}{6}$

c)

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

$c = {3}^{0} + {3}^{1} + {3}^{2} + ... + {3}^{42} = \\ = \frac{1\cdot ( {3}^{43} - 1)}{3 - 1} = \frac{{3}^{43} - 1}{2}$

d)

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

$d = 8 + {8}^{2} + {8}^{3} + ... + {8}^{88} = \\ = \frac{8\cdot ( {8}^{88} - 1)}{8 - 1} = \frac{8\cdot ( {8}^{88} - 1)}{7}$