(a) Show that, for any positive integer n. R-2 n-l n² + 3n 2n =an(n-1) - ¹) (-) + n()** for some a, 3 > 0. Give the values of a and 3. Hint: solve the above equation for a and 3, your answers should be positive numbers. (b) Find the sum the series n²+3n 2n n=0 Hint: consider using derivatives of the geometric series and part (a).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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(1) (a) Show that, for any positive integer n,
n² + 3n
=an(n − 1)
-
› (²1) ²
¹ (¹1)-¹
2n
for some a, ß> 0. Give the values of a and 3.
Hint: solve the above equation for a and 3, your answers should be positive
numbers.
(b) Find the sum the series
n²+3n
2n
n=0
Hint: consider using derivatives of the geometric series and part (a).
+ ßn
Transcribed Image Text:(1) (a) Show that, for any positive integer n, n² + 3n =an(n − 1) - › (²1) ² ¹ (¹1)-¹ 2n for some a, ß> 0. Give the values of a and 3. Hint: solve the above equation for a and 3, your answers should be positive numbers. (b) Find the sum the series n²+3n 2n n=0 Hint: consider using derivatives of the geometric series and part (a). + ßn
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