Question

c) |+2|+|+5|+|+8|+....+|+29|=
d) |-2|^1 +|-2|^2 +..... +|-2|^20=​

Answer 1

Răspuns:

c)155

d) 2²¹ - 2

Explicație pas cu pas:

c) |+ 2| + |+ 5| + |+ 8| + ...... + |+ 29| = 2 + 5 + 8 + ...... + 29

( 29 - 2 ) : 3 + 1 = 27 : 3 + 1 = 9 + 1 = 10 termeni

S = ( 2 + 29 ) x 10 : 2 = 31 x 10 : 2 = 31 x 5 = 155

d) ) |-2|^1 +|-2|^2 +..... +|-2|^20=​  2¹ + 2² + ........ + 2³ = 2 x (2²⁰ - 1) / (2 - 1) = (2²¹ - 2) / 1 = 2²¹ - 2

Answer 2

$\it c)\ \ \ = 2+5+8+\ ...\ +29=\dfrac{(2+29)\cdot10}{2}=31\cdot5=155\\ \\ \\ d)\ \ \ =2^1+2^2+2^3+\ ...\ +2^{20}=2\cdot\dfrac{2^{20}-1}{2-1}=2^{21}-2=\\ \\ \\ =(2^7)^3-3=128^3-2=2\ 097\ 152-2=2 \ 097 \ 150$