Question

Exercitiul 8, va rog. Dau coroana!

Answer 1

a)$\frac{3 ^{n+2} *5 ^{n+1} }{15 ^{n+1} } = \frac{3 ^{n+2}*5 ^{n+1} }{3 ^{n+1}*5 ^{n+1} } = \frac{3 ^{n+1}*3*5 ^{n+1} }{3 ^{n+1}*5 ^{n+1} } =3$

d)$\frac{5 ^{n}+5 ^{n+1} +5 ^{n+2} +5 ^{n+3} }{5 ^{n+1} +5 ^{n+3} } = \frac{5 ^{n}(1+5+25+125) }{5 ^{n+1}(1+25) } = \frac{5 ^{n} *156}{5 ^{n}*5*26 } = \frac{156}{130} = \frac{78}{65}$

Restul ai putea incerca si tu...

Answer 2

a) (3ⁿ⁺² ×5ⁿ⁺¹)/15ⁿ⁺¹=(3ⁿ⁺¹×3 ×5ⁿ⁺¹)/(3ⁿ⁺¹×5ⁿ⁺¹)=3
b) este rezolvat in poza
c) (5ⁿ⁺²×7ⁿ +5ⁿ×7ⁿ⁺¹)/5ⁿ⁺¹×7ⁿ⁺¹ +7ⁿ×5ⁿ⁺²)=5ⁿ×7ⁿ(5²+7)/5ⁿ×7ⁿ(5×7+1×5²)=
=(25+7)/(35+25)=32/60=8/15
d) (5ⁿ +5ⁿ⁺¹+5ⁿ⁺²+5ⁿ⁺³)/5ⁿ⁺¹ +5ⁿ⁺³)=5ⁿ(5⁰+5¹+5²+5³)/5ⁿ(5¹+5³)=
=(1+5+25+125)/(5+125)=156/130=78/65=6/5