Solution to 4. v defined by vn = n! + 2, n ≥ 1. (a) Find v3 … - Sikademy
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Archangel Macsika

4. v defined by vn = n! + 2, n ≥ 1. (a) Find v3 (b) Find Σ 4 on top , i=1 at the bottom and Vi on the right hand side of Sigma (c) Is v increasing, decreasing, non-increasing or non-decreasing?

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(a)


v_3=3!+2=8

(b)


\displaystyle\sum_{i=1}^{4}v_i=v_1+v_2+v_3+v_4

=1!+2+2!+2+3!+2+4!+2=41

(c)


v_{n+1}=(n+1)!+2>n!+2=v_n, n\geq 1

The sequence \{v_n\} is (strictly) increasing.

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