Series

WFM02Topic 2.22 questions

Summing finite series using the method of differences.

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Original practice questions written in the style of the exam.

6(n+2)(n+3)n(5n+13)

1

M1 Writes out terms for

r = 1, 2, 3, \dots

and

r = n - 1, n

to show cancellation (1)

A1 Remaining terms identified:

\tfrac{1}{2} + \tfrac{1}{3} - \dfrac{1}{n + 2} - \dfrac{1}{n + 3}

(1)

M1 Combines over the common denominator

6(n + 2)(n + 3)

(1)

A1 Numerator

5(n + 2)(n + 3) - 6(2n + 5) = 5n^2 + 13n

(1)

A1

= \dfrac{n(5n + 13)}{6(n + 2)(n + 3)}

convincingly shown (1)