1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Rufina [12.5K]
2 years ago
5

Use Gauss's approach to find the following sums (do not use formulas) a 1+2+3+4 998 b. 1+3+5 7+ 1001 a The sum of the sequence i

s
Mathematics
1 answer:
valkas [14]2 years ago
8 0

Answer:

(a) 498501

(b) 251001

Step-by-step explanation:

According Gauss's approach, the sum of a series is

sum=\frac{n(a_1+a_n)}{2}         .... (1)

where, n is number of terms.

(a)

The given series is

1+2+3+4+...+998

here,

a_1=1

a_n=998

n=998

Substitute a_1=1, a_n=998 and n=998 in equation (1).

sum=\frac{998(1+998)}{2}

sum=499(999)

sum=498501

Therefore the sum of series is 498501.

(b)

The given series is

1+3+5+7+...+ 1001

The given series is the sum of dd natural numbers.

In 1001 natural numbers 500 are even numbers and 501 are odd number because alternative numbers are even.

a_1=1

a_n=1001

n=501

Substitute a_1=1, a_n=1001 and n=501 in equation (1).

sum=\frac{501(1+1001)}{2}

sum=\frac{501(1002)}{2}

sum=501(501)

sum=251001

Therefore the sum of series is 251001.

You might be interested in
Help I’m almost out of time
VladimirAG [237]

Answer: First option.

Step-by-step explanation:

You can idenfity in the figure that \angle FCE is formed by two secants that intersect outside of the given circle.

It is important to remember that, by definition:

 Angle\ formed\ by\ two\ Secants=\frac{1}{2}( Difference\ of\ intercepted\ Arcs)

Knowing this, you can set up the following equation:

m\angle FCE=\frac{1}{2}(BD-FE)

Therefore, you must substitute values into the equation and then evaluate, in order to find the measure of the angle \angle FCE.

This is:

m\angle FCE=\frac{1}{2}(112\°-38\°)\\\\m\angle FCE=37\°

6 0
3 years ago
which shows the students in order from greatest test score to lease test score Alex 0.95 Octavia 16/20 Tonya 9/10 Wilson 0.87 ​
Nonamiya [84]

Answer:

Alex (0.95), Tonya (0.90), Wilson (0.87), Octavia (0.80)

Step-by-step explanation:

To solve this, we have to convert all of the scores into either a decimal or a fraction. In this case, I will be solving all of them into decimals since it is easier.

Alex: 0.95

Octavia: 16/20 = 0.80

Tonya: 9/10 = 0.90

Wilson: 0.87

Therefore, we can order these from greatest score to least score.

Alex (0.95), Tonya (0.90), Wilson (0.87), Octavia (0.80)

4 0
2 years ago
A) Complete the table of values for x + 2y = 7
Marrrta [24]
The values for y are as follows
4.5, 4, 3.5, 3, 2.5, 2
3 0
2 years ago
Read 2 more answers
With which set of information can you construct a unique parallelogram? Assume the parallelogram is not a rhombus, rectangle, or
FinnZ [79.3K]
I think the correct answer is b.the measurement of one angle and the lengths of two adjacent sides.
5 0
3 years ago
Read 2 more answers
PLEASE I AM IN DESPERATE NEED OF HELP
erastova [34]

Answer:

C:   H <u>> </u> 60

Step-by-step explanation:

H is 60 in or taller, underlined indicates that it's also 60 in, not just above it.

8 0
2 years ago
Other questions:
  • In order to isolate the variable term in the equation 6 - 2x = -3 using the subtraction property of equality, which number
    9·1 answer
  • The weight of the paper clip is 1.0025 grams. Find the number of significant digits in the measurement​
    8·2 answers
  • What is answer for 10+(3+4-6+8) by using order of operation
    10·2 answers
  • A teacher has a chart she would like to enlarge to put on a bulletin board. The chart is 8 cm across, and the space on the bulle
    9·2 answers
  • Jk is perpendicular to xy at its midpoint m. choose the answer that includes the correct responses.
    5·1 answer
  • Are parallelogram rectangles
    10·1 answer
  • -25-6= -25 + -6 = -31
    5·1 answer
  • PLEASE PLEASE PLEASE HELP ME Which of the following is a perfect square trinomial?
    7·1 answer
  • What is the y-intercept of this line?
    14·2 answers
  • How many diagonals will a decaoctagon have?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!