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2 years ago

Im a breadstick grrrr

Mathematics

2 answers:

STatiana [176]2 years ago

6 0

Answer:

based

Step-by-step explanation:

GrogVix [38]2 years ago

4 0

Answer:

ok if u say so

Step-by-step explanation:

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For the following telescoping series, find a formula for the nth term of the sequence of partial sums {Sn}. Then evaluate limn→[

Ivenika [448]

Answer:

The following are the solution to the given points:

Step-by-step explanation:

Given value:

$1) \sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2}\\\\2) \sum ^{\infty}_{k = 1} \frac{1}{(k+6)(k+7)}$

Solve point 1 that is $\sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2}\\\\$ :

when,

$k= 1 \to s_1 = \frac{1}{1+1} - \frac{1}{1+2}\\\\$

$= \frac{1}{2} - \frac{1}{3}\\\\$

$k= 2 \to s_2 = \frac{1}{2+1} - \frac{1}{2+2}\\\\$

$= \frac{1}{3} - \frac{1}{4}\\\\$

$k= 3 \to s_3 = \frac{1}{3+1} - \frac{1}{3+2}\\\\$

$= \frac{1}{4} - \frac{1}{5}\\\\$

$k= n^ \to s_n = \frac{1}{n+1} - \frac{1}{n+2}\\\\$

Calculate the sum $(S=s_1+s_2+s_3+......+s_n)$

$S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....\frac{1}{n+1}-\frac{1}{n+2}\\\\$

$=\frac{1}{2}-\frac{1}{5}+\frac{1}{n+1}-\frac{1}{n+2}\\\\$

When $s_n \ \ dt_{n \to 0}$

$=\frac{1}{2}-\frac{1}{5}+\frac{1}{0+1}-\frac{1}{0+2}\\\\=\frac{1}{2}-\frac{1}{5}+\frac{1}{1}-\frac{1}{2}\\\\= 1 -\frac{1}{5}\\\\= \frac{5-1}{5}\\\\= \frac{4}{5}\\\\$

$\boxed{\text{In point 1:} \sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2} =\frac{4}{5}}$

In point 2: $\sum ^{\infty}_{k = 1} \frac{1}{(k+6)(k+7)}$

when,

$k= 1 \to s_1 = \frac{1}{(1+6)(1+7)}\\\\$

$= \frac{1}{7 \times 8}\\\\= \frac{1}{56}$

$k= 2 \to s_1 = \frac{1}{(2+6)(2+7)}\\\\$

$= \frac{1}{8 \times 9}\\\\= \frac{1}{72}$

$k= 3 \to s_1 = \frac{1}{(3+6)(3+7)}\\\\$

$= \frac{1}{9 \times 10} \\\\ = \frac{1}{90}\\\\$

$k= n^ \to s_n = \frac{1}{(n+6)(n+7)}\\\\$

calculate the sum: $S= s_1+s_2+s_3+s_n\\$

$S= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{(n+6)(n+7)}\\\\$

when $s_n \ \ dt_{n \to 0}$

$S= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{(0+6)(0+7)}\\\\= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{6 \times 7}\\\\= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{42}\\\\=\frac{45+35+28+60}{2520}\\\\=\frac{168}{2520}\\\\=0.066$

$\boxed{\text{In point 2:} \sum ^{\infty}_{k = 1} \frac{1}{(n+6)(n+7)} = 0.066}$

8 0

2 years ago

The equation tan^2 x+1=sec^2 x is an identity true or false

Solnce55 [7]

Answer:

tan²x + 1 = sec²x is identity

Step-by-step explanation:

* Lets explain how to find this identity

∵ sin²x + cos²x = 1 ⇒ identity

- Divide both sides by cos²x

∵ sin x ÷ cos x = tan x

∴ sin²x ÷ cos²x = tan²x

- Lets find the second term

∵ cos²x ÷ cos²x = 1

- Remember that the inverse of cos x is sec x

∵ sec x = 1/cos x

∴ sec²x = 1/cos²x

- Lets write the equation

∴ tan²x + 1 = 1/cos²x

∵ 1/cos²x = sec²x

∴ than²x + 1 = sec²x

- So we use the first identity sin²x + cos²x = 1 to prove that

tan²x + 1 = sec²x

∴ tan²x + 1 = sec²x is identity

8 0

3 years ago

Whath percentage of 1m is 76cm

nlexa [21]

76% is the correct.....

5 0

3 years ago

What is 5/8 times 24hours

max2010maxim [7]

The answer is 5/8 x 24 is equal to 15 hours

8 0

3 years ago

In a week, 13 hens laid 65 eggs. What is the independent variable

scZoUnD [109]

Answer:

The hens are the independent variable

Step-by-step explanation:

An independent variable is something that isn't dependent on anything else. Whose laying the eggs? The hens right? So the number of eggs laid is dependent on the number of hens laying them. Basically the hens are the independent variable because the number of eggs is relying on the number of hens laying them.

5 0

2 years ago

Read 2 more answers