It is given that $ \sum_{r=1}^{n} r^3 = \frac{n^2(n+1)^2}{4} $. Find \( \sum_{r=4}^{N+3} (r-2

Question

It is given that $ \sum_{r=1}^{n} r^3 = \frac{n^2(n+1)^2}{4} $. Find $ \sum_{r=4}^{N+3} (r-2)^3 $ in terms of $N$.[3] Hence, find the largest value of $N$ for which $ \sum_{r=4}^{N+3} \left[(2r-4)^3+2^r\right] < 10^5 $.[3]

Accepted Answer

$\dfrac{(N+1)^2(N+2)^2}{4}-1$; largest $N=11$

2025 VJC Promo Q3

2025 VJC Promo Q3

Video Solution:

Solution:

Solution locked