# 2019 NYJC P2 Q1

## Timothy Gan

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##### 2019 NYJC P2 Q1

(i)

Show that $\frac{1}{\left( n-1 \right)!}-\frac{3}{n!}+\frac{2}{\left( n+1 \right)!}=\frac{A{{n}^{2}}+Bn+C}{\left( n+1 \right)!}$ where $A$, $B$ and $C$ are constants to be determined.

[2]

(ii)

Hence find $\sum\limits_{n=1}^{N}{\frac{{{n}^{2}}-2n-1}{5\left( n+1 \right)!}}$ in terms of $N$.

[3]

(iii)

Give a reason why the series $\sum\limits_{n=1}^{\infty }{\frac{{{n}^{2}}-2n-1}{5\left( n+1 \right)!}}$ converges and write down its value.

[2]

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## Students Only

Our H2 Math Tuition includes

• Question Bank with Video solutions to 1400+ questions
• Online Portal
• H2 Math Summary Notes
• Structured Curriculum and Notes
Free Stuff
Pure Math
Statistics