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Question Number 96951 by aurpeyz last updated on 05/Jun/20
prove that 1−(1/2)+(1/3)−(1/4)+(1/5)+...+((−1^(n−1) )/n)  is always positive
$${prove}\:{that}\:\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{5}}+…+\frac{−\mathrm{1}^{{n}−\mathrm{1}} }{{n}}\:\:{is}\:{always}\:{positive} \\ $$$$ \\ $$
Commented by mr W last updated on 05/Jun/20
how many times do you want to post  the same question? besides the   question is already answered. if you  don′t understand the answer, please  give feedback in the same thread as  the original question and answer,  instead of posting the same question  a second or third time. thank you!
$${how}\:{many}\:{times}\:{do}\:{you}\:{want}\:{to}\:{post} \\ $$$${the}\:{same}\:{question}?\:{besides}\:{the}\: \\ $$$${question}\:{is}\:{already}\:{answered}.\:{if}\:{you} \\ $$$${don}'{t}\:{understand}\:{the}\:{answer},\:{please} \\ $$$${give}\:{feedback}\:{in}\:{the}\:{same}\:{thread}\:{as} \\ $$$${the}\:{original}\:{question}\:{and}\:{answer}, \\ $$$${instead}\:{of}\:{posting}\:{the}\:{same}\:{question} \\ $$$${a}\:{second}\:{or}\:{third}\:{time}.\:{thank}\:{you}! \\ $$
Commented by mr W last updated on 05/Jun/20
answer in Q95473
$${answer}\:{in}\:{Q}\mathrm{95473} \\ $$
Commented by mr W last updated on 05/Jun/20
you can click on the funel icon on the  top of the screen and select “Go to  question ID” and then enter the no.  of the question you want to go to.  but in this case a command bar is  automatically generated, just tap  on it!
$${you}\:{can}\:{click}\:{on}\:{the}\:{funel}\:{icon}\:{on}\:{the} \\ $$$${top}\:{of}\:{the}\:{screen}\:{and}\:{select}\:“{Go}\:{to} \\ $$$${question}\:{ID}''\:{and}\:{then}\:{enter}\:{the}\:{no}. \\ $$$${of}\:{the}\:{question}\:{you}\:{want}\:{to}\:{go}\:{to}. \\ $$$${but}\:{in}\:{this}\:{case}\:{a}\:{command}\:{bar}\:{is} \\ $$$${automatically}\:{generated},\:{just}\:{tap} \\ $$$${on}\:{it}! \\ $$
Commented by aurpeyz last updated on 05/Jun/20
i am sorry. iam new to this platform
$${i}\:{am}\:{sorry}.\:{iam}\:{new}\:{to}\:{this}\:{platform} \\ $$
Commented by aurpeyz last updated on 05/Jun/20
how do i get to q95473?
$${how}\:{do}\:{i}\:{get}\:{to}\:{q}\mathrm{95473}? \\ $$
Answered by Sourav mridha last updated on 06/Jun/20
ln(1+x)=Σ_(n=1) ^∞ (((−1)^(n−1) )/n).x^n   now putting x=1 you get..  Σ_(n=1) ^∞ (((−1)^(n−1) )/n)=ln2≈0.693>0
$$\boldsymbol{{ln}}\left(\mathrm{1}+\boldsymbol{{x}}\right)=\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{\mathrm{n}−\mathrm{1}} }{\boldsymbol{{n}}}.\boldsymbol{{x}}^{\boldsymbol{{n}}} \\ $$$$\boldsymbol{{now}}\:\boldsymbol{{putting}}\:\boldsymbol{{x}}=\mathrm{1}\:\boldsymbol{{you}}\:\boldsymbol{{get}}.. \\ $$$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{\boldsymbol{{n}}−\mathrm{1}} }{\boldsymbol{{n}}}=\boldsymbol{{ln}}\mathrm{2}\approx\mathrm{0}.\mathrm{693}>\mathrm{0}\: \\ $$

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