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
solniwko [45]
3 years ago
8

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

Mathematics
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
2 x - 5 + 7 y - 3 = 9 x - 1 - y -8 Solve For X AND Y (SHOW WORK PLEASE)
Maru [420]

Answer:

\large\boxed{\sf x = \frac{8y+1}{7} }

\large\boxed{\sf x = \frac{7x-1}{8} }

<u>Group the Variable's</u>:

2 x - 5 + 7 y - 3 = 9 x - 1 - y -8

2x -9x + 7y +y = -1 -8 +5 + 3

-7x + 8y = -1

<u><em>From this find x and y</em></u>

<u>For X</u>

-7x + 8y = -1

-7x = -1 -8y

7x = 8y + 1

x = (8y +1)/7

<u>For Y</u>

-7x + 8y = -1

8y = -1 +7x

y = (7x -1)/8

3 0
2 years ago
Read 2 more answers
A group of 22 students participated in a race. Their scores are below: Score (points) 4–5 6–7 8–9 10–11 12–13 Number of Students
Anna71 [15]
A histogram would best represent the data.
Dot plot is a good way to show a certain trend. However, when it comes to the number of a item, in this case the number of students in a certain score range, a histogram will be the most intuitive and concise. Thus, a histogram best represent the data presented here.
6 0
3 years ago
Angela shared a cab with her friends. When they arrived at their destination, they evenly divided the $j fare
Ipatiy [6.2K]

Total  friends = 3

fare = $ J

She also paid $5 tip

So there is J amount of money splitted into 3 friends.

That means you divide J/3 .

After Angela also  pays additional tip of $5.

That means you also add 5.

So the expression for how much Angela pay in total is: J/3 + 5

3 0
3 years ago
How many permutations of the letters in the word REPLICA end in a vowel
Afina-wow [57]
<span>6*5*4*3*2*1*3=2,160
I hope this helps.
</span>
8 0
3 years ago
Consider the relation given by the graph below.
Murrr4er [49]

(a) The relation is a function because each value of x maps onto only one value of y.

(b) Domain is (-\infty, 3], range is [-1, \infty).

7 0
1 year ago
Other questions:
  • Helppppppppppp please and expalin if you can
    5·1 answer
  • the following graph shows the function f(x) and g(x): the function g(x) is obtained by adding ___ to f(x). (only input intergers
    7·1 answer
  • The LA dodgers hit the most home runs in 2014. The number of Home runs accounted for 6% of the entire major league baseball home
    13·1 answer
  • PLEASE answer this question​
    5·1 answer
  • Find the value of x (help quick)
    5·1 answer
  • Pls help me i will make u a brainest
    8·1 answer
  • Answers for the 2 boxes please ​
    14·1 answer
  • Can someone help me with part B?? I already did part A <br><br> Thank you so much :)
    14·2 answers
  • What is the answer if <br> Increase 12% by 30%
    6·2 answers
  • Determine the values of the requested variables
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!