Question Number 179773 by Acem last updated on 02/Nov/22
$${What}'{s}\:{the}\:{sum}\:{of}\:{the}\:{odd}\:{numbers} \\ $$$$\:{between}\:\mathrm{2313}\:{and}\:\mathrm{4718} \\ $$
Commented by CElcedricjunior last updated on 05/Nov/22
$$\boldsymbol{{calculons}}\:\boldsymbol{{la}}\:\boldsymbol{{somme}}\:\boldsymbol{{des}}\:\boldsymbol{{nombres}} \\ $$$$\boldsymbol{{comprises}}\:\boldsymbol{{entre}}\:\mathrm{2313}\:\boldsymbol{{et}}\:\mathrm{4718} \\ $$$$\Leftrightarrow\mathrm{2314}+\mathrm{2315}+……+\mathrm{4717} \\ $$$$=\left(\mathrm{2313}+\mathrm{1}\right)+\left(\mathrm{2313}+\mathrm{2}\right)+……\left(\mathrm{2313}+\mathrm{2404}\right) \\ $$$$=\mathrm{2313}×\mathrm{2404}+\frac{\mathrm{2404}×\mathrm{2405}}{\mathrm{2}} \\ $$$$=\mathrm{2313}×\mathrm{2404}+\mathrm{1202}×\mathrm{2405} \\ $$$$=\mathrm{8}.\mathrm{451}.\mathrm{262} \\ $$$${d}'\boldsymbol{{o}}\grave {\boldsymbol{{u}}}\:\underset{\boldsymbol{{k}}=\mathrm{2314}} {\overset{\mathrm{4717}} {\sum}}\boldsymbol{{k}}=\mathrm{8}.\mathrm{451}.\mathrm{262} \\ $$
Answered by Rasheed.Sindhi last updated on 02/Nov/22
$${Sum}\:{of}\:{odd}\:{numbers} \\ $$$$\:{between}\:\mathrm{2313}\:{and}\:\mathrm{4718}\left(\:{exclusively}\right) \\ $$$$\mathrm{2315}+\mathrm{2317}+…+\mathrm{4717} \\ $$$${a}=\mathrm{2315},{l}=\mathrm{4717},\:{d}=\mathrm{2}, \\ $$$$\:{l}={a}_{{n}} ={a}+\left({n}−\mathrm{1}\right){d}=\mathrm{2315}+\mathrm{2}\left({n}−\mathrm{1}\right)=\mathrm{4717} \\ $$$${n}=\left(\mathrm{4717}−\mathrm{2315}+\mathrm{2}\right)/\mathrm{2}=\mathrm{1202} \\ $$$$\begin{array}{|c|}{{S}_{{n}} =\frac{{n}}{\mathrm{2}}\left({a}+{l}\right)}\\\hline\end{array} \\ $$$${S}_{\mathrm{1202}} =\frac{\mathrm{1202}}{\mathrm{2}}\left(\mathrm{2315}+\mathrm{4717}\right)=\mathrm{4226232} \\ $$
Commented by Acem last updated on 02/Nov/22
$${Thanks}\:{for}\:{your}\:{efforts}\:{and}\:{writing}\:{details} \\ $$$${For}\:{me}\:{i}\:{use}\:{the}\:{sum}\:{till}\:\mathrm{1}\:{and}\:{subtract} \\ $$$$\:{Sum}=\:\left(\frac{{n}_{\mathrm{1}} }{\mathrm{2}}\right)^{\mathrm{2}} −\:\left(\frac{{n}_{\mathrm{2}} }{\mathrm{2}}\right)^{\mathrm{2}} \:;\:{n}_{{i}} \:{even} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:=\:\left(\frac{\mathrm{4718}}{\mathrm{2}}\right)^{\mathrm{2}} \:−\:\left(\frac{\mathrm{2314}}{\mathrm{2}}\right)^{\mathrm{2}} \:=\:\mathrm{4}\:\mathrm{226}\:\mathrm{232} \\ $$$$ \\ $$