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2 years ago

Consider the following set of equations Equation A; y=-x+5 Equation b ;y=6x-2

Mathematics

1 answer:

sp2606 [1]2 years ago

3 0

Step-by-step explanation:

6x-2= -x+5

6x+x=5+2

7x=7

x=1

then ,y= -1+5

y=4

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2 years ago

Determine if the series is convergent or divergent 20-15+10-5....

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Option b is correct.

The series 20-15+10-5....is Divergent

Step-by-step explanation:

Alternating series Test:

$\sum_{n=1}^{\infty} (-1)^{n-1} (b_n) =b_1-b_2+b_3-........$

$b_n>0$ satisfies:

$b_{n+1} \leq b_n$ for all n

$\lim_{n\rightarrow \infty} b_n = 0$

Then the series converges,

otherwise diverges.

Given the series: 20-15+10-5....

This is a alternating series:

$\sum_{n=1}^{\infty} (-1)^{n-1} (20-5(n-1))$

$b_n = (20-5(n-1))$

$b_{n+1} = (20-5(n+1-1)) = (20-5n)$

using the alternating series test;

$b_{n+1} \leq b_n$ for all n

$\lim_{n\rightarrow \infty} b_n = \lim_{n\rightarrow \infty} (20-5(n-1)) = -\infty$

⇒ the series diverges.

therefore, the given series i,e 20-15+10-5.... is divergent.

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3 years ago