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Sed (CoderLovesEggs) Paper 1 with Solutions · Q18

Paper 1Sequences & seriesFunctions & graphs

The function f(n)f(n) satisfies:

  • f(1)=1f(1)=1;
  • f(2n)=f(n)f(2n)=f(n) for all n≥1n\ge1;
  • f(2n+1)=f(n)2f(2n+1)=\dfrac{f(n)}2 for all n≥1n\ge1.

It follows that (∑i=12nf(i))\left(\displaystyle\sum_{i=1}^{2^n}f(i)\right) is equal to:

A2n+n+12\dfrac{2^n+n+1}2;
B2n−1+n2\dfrac{2^{n-1}+n}2;
Cn2+n+22\dfrac{n^2+n+2}2;
D2((32)n−1)2\left(\left(\dfrac32\right)^n-1\right);
E2(32)n−12\left(\dfrac32\right)^n-1.

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