then 9tm+1 is also triangular. Write each of the following numbers as the sum of three or fewer triangular numbers: 1 69, (b) (c) 185, (a) 56, (d) 287. 5. For n 1, establish the formula (2n+1)? 1 (4t,+1)-(4t,2 BUS 6 Verify that 1225 and 41,616 are simultaneously square and triangular numbers. [Hint: Finding an integer n such that g tinidmou bonincb of no n(n + 1) dutn 1225 2 ud is equivalent to solving the quadratic equation n2n- 2450 = 0.] *w 7. An oblong number counts the number of dots in a rectangular array having one more row than it has columns; the first few of these numbers are sln 01 2 02 6 03 12 04 =20 and in general, the nth oblong number is given by Оn n(n+1). Prove algebraically and geometrically that (а) On 2+4 6+ + 2n. Any oblong number is the sum of two equal 11 () : :
then 9tm+1 is also triangular. Write each of the following numbers as the sum of three or fewer triangular numbers: 1 69, (b) (c) 185, (a) 56, (d) 287. 5. For n 1, establish the formula (2n+1)? 1 (4t,+1)-(4t,2 BUS 6 Verify that 1225 and 41,616 are simultaneously square and triangular numbers. [Hint: Finding an integer n such that g tinidmou bonincb of no n(n + 1) dutn 1225 2 ud is equivalent to solving the quadratic equation n2n- 2450 = 0.] *w 7. An oblong number counts the number of dots in a rectangular array having one more row than it has columns; the first few of these numbers are sln 01 2 02 6 03 12 04 =20 and in general, the nth oblong number is given by Оn n(n+1). Prove algebraically and geometrically that (а) On 2+4 6+ + 2n. Any oblong number is the sum of two equal 11 () : :
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Number 6 please.
![then 9tm+1 is
also triangular.
Write each of the following numbers as the sum of
three or fewer triangular numbers:
1
69,
(b)
(c) 185,
(a) 56,
(d) 287.
5. For n
1, establish the formula
(2n+1)?
1
(4t,+1)-(4t,2
BUS
6
Verify that 1225 and 41,616 are simultaneously square
and triangular numbers. [Hint: Finding an integer n
such that
g
tinidmou
bonincb of
no
n(n + 1)
dutn
1225
2
ud
is equivalent to solving the quadratic equation
n2n- 2450 = 0.]
*w
7. An oblong number counts the number of dots in a
rectangular array having one more row than it has
columns; the first few of these numbers are
sln
01 2
02 6 03 12
04 =20
and in general, the nth oblong number is given by
Оn
n(n+1). Prove algebraically and geometrically
that
(а)
On 2+4 6+ + 2n.
Any oblong number is the sum of two equal
11
()
: :](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc27b03fb-27ff-4129-a29b-052f3c3c0c2f%2F89989fe1-4906-4f43-9d3d-e9efef51f462%2Fco4zn7c.jpeg&w=3840&q=75)
Transcribed Image Text:then 9tm+1 is
also triangular.
Write each of the following numbers as the sum of
three or fewer triangular numbers:
1
69,
(b)
(c) 185,
(a) 56,
(d) 287.
5. For n
1, establish the formula
(2n+1)?
1
(4t,+1)-(4t,2
BUS
6
Verify that 1225 and 41,616 are simultaneously square
and triangular numbers. [Hint: Finding an integer n
such that
g
tinidmou
bonincb of
no
n(n + 1)
dutn
1225
2
ud
is equivalent to solving the quadratic equation
n2n- 2450 = 0.]
*w
7. An oblong number counts the number of dots in a
rectangular array having one more row than it has
columns; the first few of these numbers are
sln
01 2
02 6 03 12
04 =20
and in general, the nth oblong number is given by
Оn
n(n+1). Prove algebraically and geometrically
that
(а)
On 2+4 6+ + 2n.
Any oblong number is the sum of two equal
11
()
: :
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