Answer:
The series converges.
Step-by-step explanation:
According to the alternating series test:
For a series ∑(-1)ⁿ aₙ or ∑(-1)ⁿ⁺¹ aₙ
If lim(n→∞) aₙ = 0
and aₙ is decreasing,
then the series converges.
aₙ = n² / (n³ + 1)
Since the power of the numerator is less than the power of the denominator, lim(n→∞) aₙ = 0.
Since n² / (n³ + 1) > (n+1)² / ((n+1)³ + 1), the series is decreasing. (We could also prove this by showing that the derivative is negative.)
Therefore, the series converges.
Answer:
n =22
Step-by-step explanation:
12-5=7
15-5=10
20-5=15
n-5=17
collect like terms
n=17+5
n=22
Answer:
n= -12
Step-by-step explanation:
- 2n/3 + 7=15 Subtract 7 from both sides and move all terms containing
-7 = -7 n to the right
- 2n/3 = 8 multiply both sides of equation by - 3/2
-3/2 x (-2n/3) = -3/2 x 8
n= -3/2 x 8 cancel the common factor of 3
n= -12
Answer:
100 + 20 (likely % since they are both blocks of 100 units)
Step-by-step explanation: