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Mathematical induction and trigonometric proofs — Question 181

Original QCE Vault practice · 6 marks

Q181 · Practice questionTechnology-freeComplex unfamiliar6 marks

QUESTION 181 (6 marks)

A programmable light display contains k2kk2^k lights in row k, for k=1,…,nk=1,\ldots,n.
a)
Prove by induction that ∑k=1nk2k=(n−1)2n+1+2\sum_{k=1}^n k2^k=(n-1)2^{n+1}+2.
[4 marks]
b)
A supply supports at most 600 lights. Determine the greatest number of complete rows.
[2 marks]
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