Question

1. Wyznacz wyraz an+1 ciągu o podanym wzorze ogolnym
a) an = n(kwdr) - 1
b) an = 2n - n(kwdr)
c) an = 3+n/n
d) an = 2n/n+5
e) an = 3n-4/2n+1
f) an = 2-3n/4n-5
g) an = 2n(kwdr)+3/2n+6
h) an = 4-2n(kwdr)/2n(kwdr)-1

2n(kwdr) -- 2n do potęgi 2
/ -- kreska ułamkowa

Answer 1

A) an= n² - 1
an+1=(n+1)²-1=n²+1-1=n²
b) an = 2n - n²
an+1=2(n+1)-(n+1)²=2n+2-n²-1=2n+1-n²
c) an = 3+n/n
an+1=3+n+1/n=4+n/n
d) an = 2n/n+5
an+1=2(n+1)/n+1+5=2n+2/n+6
e) an = 3n-4/2n+1/n
an+1=3(n+1)-4/2(n+1)+1/n+1=3n-1/2n+3/n+1
f) an = 2-3n/4n-5
an+1=2-3(n+1)/4(n+1)-5=2-3n+3/4n+4-5=-3n+5/4n-1
g) an = 2n²+3/2n+6
an+1=2(n+1)²+3/2(n+1)+6=2n²+3+3/2n+2+6=2n²+6/2n+8
h) an = 4-2n²/2n²-1
an+1=4-2(n+1)²/2(n+1)²-1=4-2n²+2/2n²+2=-2n²+6/2n²+2