Question 0515

Sigma Notation

2015 Paper 2 Question 4 Variant

Question

(i)

Show that

\frac{2}{4 r^2 + 8 r + 3}

can be expressed as

\frac{A}{2 r + 1} + \frac{B}{2 r + 3},

where

{A}

and

{B}

are constants to be determined.

[1]

The sum

\sum_{r=3}^n \frac{2}{4 r^2 + 8 r + 3}

is denoted by

{S_n.}

(ii)

Find an expression for

{S_n}

in terms of

{n.}

[4]

(iii)

Find the smallest values of

{n}

for which

{S_n}

is within

{10^{-2}}

of the sum to infinity.

[3]

Answer

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