The sum, ${{S}_{n}}$, of the first $n$ terms of a sequence ${{u}_{1}}$, ${{u}_{2}}$,${{u}_{3}}$, … i

Question

The sum, ${{S}_{n}}$, of the first $n$ terms of a sequence ${{u}_{1}}$, ${{u}_{2}}$,${{u}_{3}}$, … is given by ${{S}_{n}}={{n}^{2}}\left( An+B \right)$, where $A$ and $B$ are non-zero constants. Find an expression for ${{u}_{n}}$ in terms of $A$, $B$ and $n$, simplifying your answer. [3] It is also given that the second term is $6$ and the sixth term is $218$. Find the values of $A$ and $B$. [2] Determine if the sum to infinity exists. [1]

Accepted Answer

(i) u_n = A(3n²-3n+1) + B(2n-1); (ii) A=3, B=-5; (iii) sum to infinity does not exist

RI Sequences and Series tutorial 7A Q5

RI Sequences and Series tutorial 7A Q5

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