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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

$$\mathrm{S}=\mathrm{1}+\mathrm{3}−\mathrm{5}+\mathrm{7}+\mathrm{9}−\mathrm{11}+\mathrm{13}+\mathrm{15}−\mathrm{17}+\mathrm{19}+\mathrm{21}−\mathrm{23}+... \\ $$$$\mathrm{S}=\left(\mathrm{1}+\mathrm{3}−\mathrm{5}\right)+\left(\mathrm{7}+\mathrm{9}−\mathrm{11}\right)+\left(\mathrm{13}+\mathrm{15}−\mathrm{17}\right)+\left(\mathrm{19}+\mathrm{21}−\mathrm{23}\right)+ \\ $$$$\left(\mathrm{25}+\mathrm{27}−\mathrm{29}\right)+...+\left[\mathrm{6n}−\mathrm{5}+\mathrm{6n}−\mathrm{3}−\left(\mathrm{6n}−\mathrm{5}\right)\right] \\ $$$$=−\mathrm{1}+\mathrm{5}+\mathrm{11}+\mathrm{17}+\mathrm{23}+...+...+\left(\mathrm{6n}−\mathrm{7}\right) \\ $$$$=\frac{\left(−\mathrm{1}+\mathrm{6n}−\mathrm{7}\right)\mathrm{n}}{\mathrm{2}}=\mathrm{3n}^{\mathrm{2}} −\mathrm{4n} \\ $$$$\mathrm{S}=\mathrm{3n}^{\mathrm{2}} −\mathrm{4n} \\ $$

Commented by I want to learn more last updated on 22/Oct/20

Thanks sir

$$\mathrm{Thanks}\:\mathrm{sir} \\ $$

Commented by 1549442205PVT last updated on 25/Oct/20

you are welcome

$$\mathrm{you}\:\mathrm{are}\:\mathrm{welcome} \\ $$

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