Question 0514

Sigma Notation

2014 Paper 1 Question 6 Variant

Question

(a)

A sequence

{p_1, p_2, p_3, \ldots}

is given by

p_n = \frac{1}{3} ( 3 - 4^n ) \textrm{ for } n \geq 1.

Find

\sum_{r=1}^n p_r.

[3]

(b)

The sum,

{S_n,}

of the first

{n}

terms of a sequence

{u_1, u_2, u_3, \ldots}

is given by

S_n = 6 - \frac{1}{(n + 5)!}.

(bi)

Give a reason why the series

{\sum u_r}

converges, and write down the value of the sum to infinity.

[2]

(bii)

Find a formula for

{u_n}

in simplified form.

[2]

Answer

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