Question Number 119107 by I want to learn more last updated on 22/Oct/20
Answered by 1549442205PVT last updated on 22/Oct/20
![S=1+3−5+7+9−11+13+15−17+19+21−23+... S=(1+3−5)+(7+9−11)+(13+15−17)+(19+21−23)+ (25+27−29)+...+[6n−5+6n−3−(6n−5)] =−1+5+11+17+23+...+...+(6n−7) =(((−1+6n−7)n)/2)=3n^2 −4n S=3n^2 −4n](https://www.tinkutara.com/question/Q119113.png)
$$\mathrm{S}=\mathrm{1}+\mathrm{3}−\mathrm{5}+\mathrm{7}+\mathrm{9}−\mathrm{11}+\mathrm{13}+\mathrm{15}−\mathrm{17}+\mathrm{19}+\mathrm{21}−\mathrm{23}+… \\ $$$$\mathrm{S}=\left(\mathrm{1}+\mathrm{3}−\mathrm{5}\right)+\left(\mathrm{7}+\mathrm{9}−\mathrm{11}\right)+\left(\mathrm{13}+\mathrm{15}−\mathrm{17}\right)+\left(\mathrm{19}+\mathrm{21}−\mathrm{23}\right)+ \\ $$$$\left(\mathrm{25}+\mathrm{27}−\mathrm{29}\right)+…+\left[\mathrm{6n}−\mathrm{5}+\mathrm{6n}−\mathrm{3}−\left(\mathrm{6n}−\mathrm{5}\right)\right] \\ $$$$=−\mathrm{1}+\mathrm{5}+\mathrm{11}+\mathrm{17}+\mathrm{23}+…+…+\left(\mathrm{6n}−\mathrm{7}\right) \\ $$$$=\frac{\left(−\mathrm{1}+\mathrm{6n}−\mathrm{7}\right)\mathrm{n}}{\mathrm{2}}=\mathrm{3n}^{\mathrm{2}} −\mathrm{4n} \\ $$$$\mathrm{S}=\mathrm{3n}^{\mathrm{2}} −\mathrm{4n} \\ $$
Commented by I want to learn more last updated on 22/Oct/20
$$\mathrm{Thanks}\:\mathrm{sir} \\ $$
Commented by 1549442205PVT last updated on 25/Oct/20
$$\mathrm{you}\:\mathrm{are}\:\mathrm{welcome} \\ $$