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Write-the-first-five-series-indicating-the-5th-term-5th-partial-sum-n-1-t-n-where-t-n-1-for-n-1-1-2-for-n-2-




Question Number 27685 by NECx last updated on 13/Jan/18
Write the first five series indicating  the 5th term,5th partial sum    Σ_(n=1) ^∞ t_n , where  t_n = { ((1                                    for n=1)),(((1/2)                                  for n=2)),((1−(1/2)+...+(−1)^(n+1) ((1/n))   for   n>2)) :}
$${Write}\:{the}\:{first}\:{five}\:{series}\:{indicating} \\ $$$${the}\:\mathrm{5}{th}\:{term},\mathrm{5}{th}\:{partial}\:{sum} \\ $$$$ \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{t}_{{n}} ,\:{where} \\ $$$${t}_{{n}} =\begin{cases}{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{for}\:{n}=\mathrm{1}}\\{\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{for}\:{n}=\mathrm{2}}\\{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}+…+\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} \left(\frac{\mathrm{1}}{{n}}\right)\:\:\:{for}\:\:\:{n}>\mathrm{2}}\end{cases} \\ $$
Commented by NECx last updated on 12/Jan/18
The three t_n  are meant to be joined  but I dont know how to write it  with the app editor.
$${The}\:{three}\:{t}_{{n}} \:{are}\:{meant}\:{to}\:{be}\:{joined} \\ $$$${but}\:{I}\:{dont}\:{know}\:{how}\:{to}\:{write}\:{it} \\ $$$${with}\:{the}\:{app}\:{editor}. \\ $$
Commented by prakash jain last updated on 12/Jan/18
You can rows or columns. press line and  matrix option on the left side.
$$\mathrm{You}\:\mathrm{can}\:\mathrm{rows}\:\mathrm{or}\:\mathrm{columns}.\:\mathrm{press}\:\mathrm{line}\:\mathrm{and} \\ $$$$\mathrm{matrix}\:\mathrm{option}\:\mathrm{on}\:\mathrm{the}\:\mathrm{left}\:\mathrm{side}. \\ $$

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