3. Prove each identity below by counting a set in two ways (without manipulating the formulae). 2n = 2 (ii) 2-1 n- i) S---1 q" – 1 for q, n eN i(n-i): (iv) v) 1+ 2+ 4+ + 2-1+ 2" = 3" n-

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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3. Prove each identity below by counting a set in two ways (without manipulating the formulae).
2n
= 2
(ii)
2-1
n-
i)
S---1
q" – 1
for q, n eN
i(n-i):
(iv)
v) 1+
2+
4+ +
2-1+
2"
= 3"
n-
Transcribed Image Text:3. Prove each identity below by counting a set in two ways (without manipulating the formulae). 2n = 2 (ii) 2-1 n- i) S---1 q" – 1 for q, n eN i(n-i): (iv) v) 1+ 2+ 4+ + 2-1+ 2" = 3" n-
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