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Paper 2 · November 2017 · Mathematical induction

For the statement $\displaystyle\sum_{r=1}^{n}(r+1)2^{r}=n2^{n+1}$ , evaluate the left hand side when $n=1$ .

Model answer

4

Explanation

With

n=1

the sum has the single term

r=1

, which is

(1+1)2^{1}=4

. (The right hand side is

1\times2^{2}=4

as well, so the base case holds.)

Derived from ZIMSEC Mathematics Paper 2, November 2017, Q1

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