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)) :}


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Question Number 27685 by NECx last updated on 13/Jan/18
$Write the first five series indicating the 5th term,5th partial sum Σ_(n=1) ^∞ t_n , where t_n = { ((1 for n=1)),(((1/2) for n=2)),((1−(1/2)+...+(−1)^(n+1) ((1/n)) for n>2)) :}$
$W r i t e t h e f i r s t f i v e s e r i e s i n d i c a t i n g$ $t h e 5 t h t e r m, 5 t h p a r t i a l s u m$ $\underset{n = 1}{\sum^{\infty}} t_{n}, w h e r e$ $t_{n} = {\begin{cases} 1 f o r n = 1 \\ \frac{1}{2} f o r n = 2 \\ 1 - \frac{1}{2} + . . . + {(- 1)}^{n + 1} (\frac{1}{n}) f o r n > 2 \end{cases}$
Commented by NECx last updated on 12/Jan/18

$T h e t h r e e t_{n} a r e m e a n t t o b e j o i n e d$ $b u t I d o n t k n o w h o w t o w r i t e i t$ $w i t h t h e a p p e d i t o r .$
Commented by prakash jain last updated on 12/Jan/18

$You can rows or columns . press line and$ $matrix option on the left side .$
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