All categories

3 years ago

Use Gauss's approach to find the following sums (do not use formulas). 1+3+5+7+...+1001

1 answer:

kramer3 years ago

5 0

Hello,

$s=1+2+3+...+1000+1001=\sum_{i=1}^{1001}\ i \ (1) \\ 

s=1001+1000+...+3+2+1=\sum_{j=1}^{1001}\ 1002-j \ (2)\\

(1)+(2)==\textgreater \ 2*s=(1+1001)+(2+1000)+...+(1000+2)+(1001+1)\\

=1002*1001=(\sum_{i=1}^{1001}\ i )\ +(\sum_{i=1}^{1001}\ 1002-i )\ \\

=\sum_{i=1}^{1001}\ ( i+1002-i)\ = \sum_{i=1}^{1001}\ 1002=1001*1002\\

So\ s= \dfrac{1001*1002}{2} =501501\\
 




$

You might be interested in

A new screening test for Lyme disease is developed for use in the general population. The sensitivity and specificity of the new

Anit [1.1K]

Answer:

predictive value of a positive test = 18.18%

predictive value of a negative test = 94.03%

Step-by-step explanation:

Sensitivity = 60% = 0.6

Specificity = 70% = 0.7

Let True Positive = TP

True Negative = TN

False Negative = FN

$Sensitivity = \frac{TP}{TP + FN} \\0.6 = \frac{TP}{TP + FN} \\0.6TP + 0.6FN = TP\\0.4TP = 0.6FN\\TP = 1.5 FN$

$Specificity = \frac{TN}{TN + FP} \\0.7 = \frac{TN}{TN + FP} \\0.7TN + 0.7FP = TN\\0.7FP = 0.3 TN\\TN = 7/3 FP$

Prevalence = 10% = 0.1

Three hundred people are screened, $T_{total} = 300$

Total number of people having the disease, $T_{disease} = ?$

$Prevalence = \frac{T_{disease} }{T_{total} } \\0.1 = \frac{T_{disease} }{300 }\\T_{disease} = 30$

$T_{disease} = TP + FN\\30 = TP + FN$

But TP = 1.5 FN

30 = 1.5 FN + FN

30 = 2.5 FN

FN = 30/2.5

FN = 12

TP = 1.5 FN = 1.5 * 12

TP = 18

$FP + TN = T_{total} - T_{disease} \\FP + TN = 300 - 30\\FP + TN = 270\\FP + \frac{7}{3} FP = 270\\\frac{10}{3} FP = 270\\FP = 27 * 3\\FP = 81$

81 + TN = 270

TN = 189

To calculate the Predictive value of positive test (PPT)

$PPT = \frac{TP}{TP + FP} * 100\\PPT = \frac{18}{18+81} * 100\\PPT = \frac{18}{99} * 100\\PPT = 18.18 \%$

To calculate the Predictive value of negative test (PNT)

$PPT = \frac{TN}{FN + TN} * 100\\PPT = \frac{189}{189+12} * 100\\PPT = \frac{189}{201} * 100\\PPT = 94.03 \%$

7 0

3 years ago

Find the square root. −2.25−−−−√

Andreas93 [3]

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

1.5

1.5i

6 0

2 years ago

Help please like PLEASE ASAP

FromTheMoon [43]

Answer:

1/5^5

Step-by-step explanation:

Flip the equation into a fraction.

5 0

3 years ago

Read 2 more answers

30.

zaharov [31]

There are two triangles in the figure(triangular prism) option third is correct.

<h3>What is a triangular prism?</h3>

When a triangle is, stretch it out to produce a stack of triangles, one on top of the other. A triangular prism is a name given to this novel 3D object.

The complete question is:

How many triangles are needed to draw the net of this object?

For the figure please refer to the attached picture.

As we can see in the figure we have given a triangular prism:

The triangular prism has two triangles.

A triangle for the base of the prism and a triangle for the top of the prism.

The lateral faces of the prism are rectangular.

Thus, there are two triangles in the figure(triangular prism) option third is correct.

Learn more about triangular prisms here:

brainly.com/question/16909441

#SPJ1

3 0

2 years ago

Pettit printing company has a total market value of $100 million, consisting of 1 million shares selling for $50 per share and $

amm1812

The weighted average cost of capital for the firm will be 11.25%.

<h3>How to calculate the WACC?</h3>

The weighted average cost of capital is the calculation of the cost of capital for a firm where each category of capital is weighted.

Here, the weighted average cost of capital will be:

= 0.5(10%)(1 - 15%) + 0.5(14%)

= 0.5(0.1)(0.85) + 0.5(0.14)

= 11.25%

The corporate value at 70% debt when WACC is 11.94% will be:

= (EBIT)(1 - T)/WACC

= (13.24)(1 - 0.15)/0.1194

= $94.26 million

The corporate value at 30% debt when WACC is 11.14% will be:

= (EBIT)(1 - T)/WACC

= (13.24)(1 - 0.15)/0.1114

= $101.02 million

Learn more about WACC on:

brainly.com/question/25566972

#SPJ1

4 0

1 year ago

Use​ Gauss's approach to find the following sums​ (do not use​ formulas). 1+3+5+7+...+1001

Use Gauss's approach to find the following sums (do not use formulas). 1+3+5+7+...+1001