Instructions
Click the button below to start.
Parts (i)-(iii) will stay the same. Part (iv) will be changed each time you click the button again.
Practice until you can perform the "substitution" technique reliably.
Question
A sequence un is defined by un=1n3 for n∈Z,n≥1.
- Show that un−un+1=3n2+3n+1n3(n+1)3.
- Hence find N∑n=13n2+3n+1n3(n+1)3.
- Give a reason why the series in part (ii) is convergenet and state the sum to infinity.
- Use your answer to part (ii) to find 1
Answer
- 1−1(N+1)3.
- As N→∞, 1(N+1)3→0. 1−1(N+1)3→1 so the series is convergent and the sum to infinity is 1.
- 2