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Question-193204

Question Number 193204 by Mingma last updated on 07/Jun/23 Answered by witcher3 last updated on 08/Jun/23 $$\mathrm{H}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{k}}=\overset{\mathrm{1}} {\int}_{\mathrm{0}} \underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{x}^{\mathrm{k}−\mathrm{1}} \mathrm{dx}…

Question-193203

Question Number 193203 by Mingma last updated on 07/Jun/23 Answered by som(math1967) last updated on 07/Jun/23 $$\frac{{DB}}{{DC}}=\frac{{BE}}{{EC}}\:\:\left[{DE}\:{is}\:{bisector}\:{of}\angle{BDC}\right] \\ $$$$\:\frac{{DB}}{{DC}}=\frac{\mathrm{1}}{\mathrm{2}}\: \\ $$$${Sin}\angle{DCB}={Sin}\mathrm{30} \\ $$$$\angle{DCB}=\mathrm{30} \\ $$$$\:\frac{{DB}}{{BC}}={tan}\mathrm{30}…

a-1-a-2-a-n-are-mutually-distinct-and-is-a-am-sequence-if-a-1-a-2-a-n-A-and-a-1-2-a-2-2-a-n-2-B-find-the-am-sequence-

Question Number 193199 by mnjuly1970 last updated on 07/Jun/23 $$ \\ $$$$\:\:\:{a}_{\mathrm{1}} \:,\:{a}_{\mathrm{2}} \:,…,{a}_{{n}} \:{are}\:\:{mutually}\:{distinct} \\ $$$$\:\:{and}\:{is}\:{a}\:\:\:\:{am}\:\:{sequence}\:. \\ $$$$\:\:\:{if}\:{a}_{\:\mathrm{1}} \:+{a}_{\:\mathrm{2}} \:+…+{a}_{{n}} \:={A} \\ $$$$\:\:\:{and}\:\: \\…

Choose-the-correct-option-If-a-b-and-c-are-consecutive-positive-integers-and-log-1-ac-2k-then-the-value-of-k-is-a-log-a-b-log-b-c-2-d-1-Give-the-explaination-also-

Question Number 193230 by MATHEMATICSAM last updated on 07/Jun/23 $$\boldsymbol{\mathrm{Choose}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{correct}}\:\boldsymbol{\mathrm{option}}: \\ $$$$\mathrm{If}\:{a},\:{b}\:\mathrm{and}\:{c}\:\mathrm{are}\:\mathrm{consecutive}\:\mathrm{positive} \\ $$$$\mathrm{integers}\:\mathrm{and}\:\mathrm{log}\left(\mathrm{1}\:+\:{ac}\right)\:=\:\mathrm{2}{k}\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:{k}\:\mathrm{is}: \\ $$$$\left.\mathrm{a}\right)\:\mathrm{log}\:{a} \\ $$$$\left.\mathrm{b}\right)\:\mathrm{log}\:{b} \\ $$$$\left.\mathrm{c}\right)\:\mathrm{2} \\ $$$$\left.\mathrm{d}\right)\:\mathrm{1} \\…

solve-and-solution-sin-1-x-dx-

Question Number 193192 by 073 last updated on 07/Jun/23 $$\mathrm{solve}\:\mathrm{and}\:\mathrm{solution} \\ $$$$\Omega=\int\sqrt{\mathrm{sin}^{−\mathrm{1}} \mathrm{x}}\mathrm{dx}=? \\ $$ Answered by Frix last updated on 07/Jun/23 $$\int\sqrt{\mathrm{sin}^{−\mathrm{1}} \:{x}}\:{dx}\:\overset{\left[{t}=\mathrm{sin}^{−\mathrm{1}} \:{x}\right]}…