Answer:
[4, 6]
Step-by-step explanation:
∑ₙ₌₁°° (x − 5)ⁿ / n²
Use ratio test.
lim(n→∞)│aₙ₊₁ / aₙ│< 1
lim(n→∞)│[(x − 5)ⁿ⁺¹ / (n+1)²] / [(x − 5)ⁿ / n²]│< 1
lim(n→∞)│[(x − 5) n² / (n+1)²│< 1
│x − 5│< 1
-1 < x − 5 < 1
4 < x < 6
If x = 4, ∑ₙ₌₁°° (4 − 5)ⁿ / n² = ∑ₙ₌₁°° (-1)ⁿ / n², which converges.
If x = 6, ∑ₙ₌₁°° (6 − 5)ⁿ / n² = ∑ₙ₌₁°° 1 / n², which converges.
So the interval of convergence is [4, 6].
Combine like terms 14n+2k
The sum of two irrational numbers, in some cases, will be irrational.
Mrs Prescott baked 24 cookies
24/6=4 4 represents 1 sixth
5 sixths are oatmeal, 5x4=20
20 cookies are oatmeal cookies
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Answer: $107
Step-by-step explanation:
Tip = 20 % of $90
= 20/100 × $90
=$18
Sales tax at 10% = 10/100 × $90
= $9
Total cost= $90 + $18 + $9
= $107