Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
24. The nth pyramid number, P is the number of balls of equal diameter that can be stacked in a pyramid whose base is an n by n square. The first few pyramid numbers are p, = 1,p2=5.P3=14, and P4= 30. A pyramid of p3 = 55 balls is in the figure at the right. Show that n(n + 1)(2n + 1) (a) Pa=1²+2² + ……+n² = for every natural number n.

24. The nth pyramid number, P is the number of balls of equal diameter that can be stacked in a pyramid whose base is an n by n square. The first few pyramid numbers are p, = 1,p2=5.P3=14, and P4= 30. A pyramid of p3 = 55 balls is in the figure at the right. Show that n(n + 1)(2n + 1) (a) Pa=1²+2² + ……+n² = for every natural number n.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

i solved b c and d by substituting  the n to the number 2 3 and 4 i dont know whether this is good proof or not. Maybe i should use PCI? Can you help me on this?　ｃａｕｓｅ　ｉ’ｖｅ　ｂｅｅｎ　ｓｔｕｃｋ　ｏｎ　ｔｈｉｓ．　ｔｈａｎｋｓ　ａ　ｌｏｔ． 

24. The nth pyramid number, Pr is the number of balls of equal diameter that can be stacked in a pyramid whose base is an n by n square. The first few pyramid numbers are p, = 1,p2= 5, p3= 14, and P4 = 30. A pyramid of ps = 55 balls is in the figure at the right. Show that n(n + 1)(2n + 1) (a) Pa=12+2² + ……+n² = for every natural number n. *.. n+ (b) Pa= -(*:") - (";'). + for n > 2. 12n + Pa = (c) for all natural numbers n. + 1 for n> 2. (d) P.= n
Transcribed Image Text:24. The nth pyramid number, Pr is the number of balls of equal diameter that can be stacked in a pyramid whose base is an n by n square. The first few pyramid numbers are p, = 1,p2= 5, p3= 14, and P4 = 30. A pyramid of ps = 55 balls is in the figure at the right. Show that n(n + 1)(2n + 1) (a) Pa=12+2² + ……+n² = for every natural number n. *.. n+ (b) Pa= -(*:") - (";'). + for n > 2. 12n + Pa = (c) for all natural numbers n. + 1 for n> 2. (d) P.= n
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS