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Svet_ta [14]
2 years ago
9

Solve this Inequality 1 > -1 - w

Mathematics
1 answer:
Rom4ik [11]2 years ago
8 0

Answer:

\displaystyle -2 < w

Step-by-step explanation:

1 > −1 - w

+ 1 + 1

________

\displaystyle \frac{2}{-1} > \frac{-w}{-1} \\ \\ -2 < w

Whenever you divide\multiply by a <em>negative</em>, you reverse the inequality symbol.

I am joyous to assist you anytime.

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Which of the following series are convergent?
Westkost [7]

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.

3 0
3 years ago
Factorise<br>b^3−b^2+b−1,2b^3−b^2+b−2​
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Answer:

(b² + 1) (b - 1)

Step-by-step explanation:

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= b² (b - 1) + 1(b - 1)

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2 years ago
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Answer:

66

Step-by-step explanation:

The bases are both the same so it's 3*3 for both of them.

The sides are also the same so it's 3*4 for all four of them.

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