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If f(x) = at a + √a 2n-1 "I 2f ( 217 ) Σ r=1 (a) 1 (a > 0), then the value of (b) 2n

If f(x) = at a + √a 2n-1 "I 2f ( 217 ) Σ r=1 (a) 1 (a > 0), then the value of (b) 2n

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
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Let f(x) be a function satisfying the functional equation f(x) + f(1 − x) = k, for every x € Q, where k is a constant quantity. Let m be a positive integer. Π Π Π Π Put x = r m + 1 1 \m + 1/ _ \ m+ 1 ΣπF)+Σ,+1=5) m r=l m in the given equation we get r=1 m Σ(+)+2+1) m Σ AMF) r=1 m + 1 m where t = m + 1 - r. m 22 FF 1) r=1 + = mk m mk 2 m = mk = mk
Transcribed Image Text:Let f(x) be a function satisfying the functional equation f(x) + f(1 − x) = k, for every x € Q, where k is a constant quantity. Let m be a positive integer. Π Π Π Π Put x = r m + 1 1 \m + 1/ _ \ m+ 1 ΣπF)+Σ,+1=5) m r=l m in the given equation we get r=1 m Σ(+)+2+1) m Σ AMF) r=1 m + 1 m where t = m + 1 - r. m 22 FF 1) r=1 + = mk m mk 2 m = mk = mk
If f(x) = at a + √a 2n-1 "I 2f ( 217 ) Σ r=1 (a) 1 (c) 2n-1 (a > 0), then the value of (b) 2n (d) (2n-1) 2.
Transcribed Image Text:If f(x) = at a + √a 2n-1 "I 2f ( 217 ) Σ r=1 (a) 1 (c) 2n-1 (a > 0), then the value of (b) 2n (d) (2n-1) 2.
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