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
balu736 [363]
3 years ago
6

Please help me out! (show all work)

Mathematics
1 answer:
Brums [2.3K]3 years ago
3 0
First verify it holds for n=1
then you are allowed to assume it holds for n and you can start with the induction step

for n+1 instead of inserting it into the equation, add it to both sides and transform it to the original formula to proof its equality

1^{2}+2^{2}+3^{2}+...+n^{2}+(n+1)^{2}=\frac{n(n+1)(2n+1)}{6} +(n+1)^{2} \\ =\frac{n(n+1)(2n+1)+6(n+1)^{2} }{6}\\ =\frac{n(n+1)(2n+1)+6(n+1)(n+1)}{6}\\ =\frac{(n+1)(n(2n+1)+6(n+1))}{6}\\ =\frac{(n+1)((2n^{2}+n)+6(n+1))}{6}\\ =\frac{(n+1)(2n^{2}+7n+6)}{6}\\ =\frac{(n+1)(n+2)(2n+3)}{6}\\ =\frac{(n+1)((n+1)+1)(2(n+1)+1)}{6}

this equals the original formula if you had inserted n+1, proving the correctness
You might be interested in
NEED HELP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
vodomira [7]
Y=5/2x-20
There’s answer
6 0
4 years ago
What is the answer to the math problem 5+9(2+4)?
IceJOKER [234]

Answer:

59

Step-by-step explanation:

Simplify the following:

5 + 9 (2 + 4)

2 + 4 = 6:

5 + 9×6

9×6 = 54:

5 + 54

5 + 54 = 59:

Answer:  59

6 0
3 years ago
Read 2 more answers
Use the dot product to find |v| when v = (-2,-1)<br> a. -1<br> b. -3<br> C. Root 5<br> D. Root 3
Firdavs [7]
Answer
Root 5 for sure
5 0
3 years ago
Given ü=&lt;4,-1 &gt; and =&lt; 3,2 &gt;
Galina-37 [17]

Answer:

idk

Step-by-step explanation:

6 0
3 years ago
PLEASE HELP. I don't understand! I will give brainliest!
bezimeni [28]

Answer:

A is Y equally X

B is X equally 2

E is Y equally -5

6 0
3 years ago
Other questions:
  • Determine the quadrant where θ lies given that sinθ &lt; 0 and tanθ &gt; 0.
    10·2 answers
  • DONT KEEP SCROLLING PLEASE<br><br> Please I don’t understand 50 POINTS BRAINLIEST
    10·1 answer
  • What is the difference between fraction and operation ​
    13·1 answer
  • Mt. McKinley, which is the highest elevation in North America, is 20,320 feet above sea level. Death Valley, which is the lowest
    14·1 answer
  • Determine the coordinates of the midpoint M of line segment AB, formed by connecting points A(1.5, 3.2) and B(2.7, -6.8). In oth
    8·1 answer
  • How much would the combined production of pineapples increase for the two islands due to trade? How much would the combined prod
    14·1 answer
  • A student usually saves $20 a month. He would like to reach a goal of saving $350 in 12 months. The student writes the equation
    11·1 answer
  • When y varies proportionally with x, what is k when x = 50 and y = 375?
    9·1 answer
  • A rectangular field is 1/3 as wide as it is long and is enclosed by x yards of fencing. What is the area of the field in terms o
    11·1 answer
  • Write the following ratios 750 ml: 3L​
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!