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

$$\mathrm{write}2\times 7+3\times 84\times 9+5\times 10+6\times 11\mathrm{using}\mathrm{the}\mathrm{sigma}$$$$\mathrm{notation}$$

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

$$let{S}_n=\sum _{k=1}^{n}k(k+5)\Rightarrow S_n=\sum _{k=1}^n{k}^2+5\sum _{k=1}^{n}k$$$$=\frac{n(n+1)(2n+1)}{2}+5\frac{n(n+1)}{2}\Rightarrow$$$$\sum _{k=2}^{6}k(k+5)=\sum _{k=1}^{6}k(k+5)-6=\frac{6.7.13}{2}+5\frac{6.7}{2}-6$$$$=21.13+5.21-6=21\times 13)+105-6=21\times 13+99=....$$

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