ELEME 4. Prove that the square of any odc specifically, that In the sequence of triangular nu (a) Two triangular numbers whe (b) Three successive triangular (c) Three successive triangular 6. (a) If the triangular number t, is (b) Use part (a) to find three exa 7. Show that the difference between always a cube. & Prove that the sum of the reciproc is, 1 1 [Hint: Observe that = 2(- (a) Establish the identity t = ty + n(n + 3) and n > 1, thereby proving that the sum of two other such numb O Find three examples of triangu. numbers. ch of the numbers 1,5 1+4, 12 = 1 %3D sents the number of dots that can

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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2.1 question 8

ELEME
4. Prove that the square of any odc
specifically, that
In the sequence of triangular nu
(a) Two triangular numbers whe
(b) Three successive triangular
(c) Three successive triangular
6. (a) If the triangular number t, is
(b) Use part (a) to find three exa
7. Show that the difference between
always a cube.
& Prove that the sum of the reciproc
is,
1
1
[Hint: Observe that = 2(-
(a) Establish the identity t = ty +
n(n + 3)
and n > 1, thereby proving that
the sum of two other such numb
O Find three examples of triangu.
numbers.
ch of the numbers
1,5 1+4, 12 = 1
%3D
sents the number of dots that can
Transcribed Image Text:ELEME 4. Prove that the square of any odc specifically, that In the sequence of triangular nu (a) Two triangular numbers whe (b) Three successive triangular (c) Three successive triangular 6. (a) If the triangular number t, is (b) Use part (a) to find three exa 7. Show that the difference between always a cube. & Prove that the sum of the reciproc is, 1 1 [Hint: Observe that = 2(- (a) Establish the identity t = ty + n(n + 3) and n > 1, thereby proving that the sum of two other such numb O Find three examples of triangu. numbers. ch of the numbers 1,5 1+4, 12 = 1 %3D sents the number of dots that can
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