write-2-7-3-8-4-9-5-10-6-11-using-the-sigma-notation-

Question Number 43341 by pieroo last updated on 10/Sep/18

write 2 \times 7 + 3 \times 8 4 \times 9 + 5 \times 10 + 6 \times 11 using the sigma

notation

Answered by $@ty@m last updated on 10/Sep/18

\underset{n = 2}{\sum^{6}} n (n + 5)

Commented by maxmathsup by imad last updated on 10/Sep/18

l e t S_{n} = \sum_{k = 1}^{n} k (k + 5) \Rightarrow S_{n} = \sum_{k = 1}^{n} k^{2} + 5 \sum_{k = 1}^{n} k

= \frac{n (n + 1) (2 n + 1)}{2} + 5 \frac{n (n + 1)}{2} \Rightarrow

\sum_{k = 2}^{6} k (k + 5) = \sum_{k = 1}^{6} k (k + 5) - 6 = \frac{6.7.13}{2} + 5 \frac{6.7}{2} - 6

= 21.13 + 5.21 - 6 = 21 \times 13) + 105 - 6 = 21 \times 13 + 99 = \dots .