Answer:
All of them
Step-by-step explanation:
According to the ratio test, for a series ∑aₙ:
If lim(n→∞) |aₙ₊₁ / aₙ| < 1, then ∑aₙ converges.
If lim(n→∞) |aₙ₊₁ / aₙ| > 1, then ∑aₙ diverges.
(I) aₙ = 10 / n!
lim(n→∞) |(10 / (n+1)!) / (10 / n!)|
lim(n→∞) |(10 / (n+1)!) × (n! / 10)|
lim(n→∞) |n! / (n+1)!|
lim(n→∞) |1 / (n+1)|
0 < 1
This series converges.
(II) aₙ = n / 2ⁿ
lim(n→∞) |((n+1) / 2ⁿ⁺¹) / (n / 2ⁿ)|
lim(n→∞) |((n+1) / 2ⁿ⁺¹) × (2ⁿ / n)|
lim(n→∞) |(n+1) / (2n)|
1/2 < 1
This series converges.
(III) aₙ = 1 / (2n)!
lim(n→∞) |(1 / (2(n+1))!) / (1 / (2n)!)|
lim(n→∞) |(1 / (2n+2)!) × (2n)! / 1|
lim(n→∞) |(2n)! / (2n+2)!|
lim(n→∞) |1 / ((2n+2)(2n+1))|
0 < 1
This series converges.
6 × 10^-10
Hope this helps
Answer:
Step-by-step explanation:
<h3>Hope it is helpful...</h3>
I think it would be 90? Wait for other answers by smarter people than me haha.
1 purse and 1 watch is 27€
2 purse and 1 watch is 41€
So we can see the watch is constant means 1 watch is every time but purse is increase by 1 in the next expression
So 41-27 = 14€ is one purse
because the watch is every time one, so the next value increase is by purse
1purse and 1watch = 27
We know,
1 purse is 14€
So 27-14=13€ is one watch
We can check by
1 purse is 14 so two purse is 14*2=28
28+13=41
Which is same as they said in second expression
Hope it help you!¡
