Simplify $\frac{1}{15} + \frac{1}{35} + \frac{1}{63} + \frac{1}{99} + \frac{1}{143}$ $1/15+1/35+1/63+1/99+1/143$ ?

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Simplify $\frac{1}{15} + \frac{1}{35} + \frac{1}{63} + \frac{1}{99} + \frac{1}{143}$ $1/15+1/35+1/63+1/99+1/143$ ?

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Answer 1 · 2017-10-27T10:34:30

$\frac{1}{15} + \frac{1}{35} + \frac{1}{63} + \frac{1}{99} + \frac{1}{143} = \frac{5}{39}$ $1/15+1/35+1/63+1/99+1/143=5/39$

Explanation:

$\frac{1}{15} + \frac{1}{35} + \frac{1}{63} + \frac{1}{99} + \frac{1}{143}$ $1/15+1/35+1/63+1/99+1/143$

= $\frac{1}{3 \times 5} + \frac{1}{5 \times 7} + \frac{1}{7 \times 9} + \frac{1}{9 \times 11} + \frac{1}{11 \times 13}$ $1/(3xx5)+1/(5xx7)+1/(7xx9)+1/(9xx11)+1/(11xx13)$

= $\frac{7 \times 9 \times 11 \times 13 + 3 \times 9 \times 11 \times 13 + 3 \times 5 \times 11 \times 13 + 3 \times 5 \times 7 \times 13 + 3 \times 5 \times 7 \times 9}{3 \times 5 \times 7 \times 9 \times 11 \times 13}$ $(7xx9xx11xx13+3xx9xx11xx13+3xx5xx11xx13+3xx5xx7xx13+3xx5xx7xx9)/(3xx5xx7xx9xx11xx13)$

= $\frac{9009 + 3861 + 2145 + 1365 + 945}{135135}$ $(9009+3861+2145+1365+945)/135135$

= $\frac{17325}{135135}$ $17325/135135$

= $\frac{3465}{27027}$ $3465/27027$ - dividing by $5$ $5$

= $\frac{385}{3003}$ $385/3003$ - dividing ny $9$ $9$

= $\frac{35}{273}$ $35/273$ - dividing by $11$ $11$

= $\frac{5}{39}$ $5/39$ - dividing by $7$ $7$

Answer 2 · 2017-10-27T12:13:40

5/39

Explanation:

Given, $\frac{1}{15} + \frac{1}{35} + \frac{1}{63} + \frac{1}{99} + \frac{1}{143}$ $1/15+1/35+1/63+1/99+1/143$

First of all multiply Numerator and Denumerator by 2/2 and we get,

$\Rightarrow \frac{2}{2} (\frac{1}{15} + \frac{1}{35} + \frac{1}{63} + \frac{1}{99} + \frac{1}{143})$ $rArr 2/2(1/15+1/35+1/63+1/99+1/143)$

$\Rightarrow \frac{1}{2} (\frac{2}{15} + \frac{2}{35} + \frac{2}{63} + \frac{2}{99} + \frac{2}{143})$ $rArr 1/2(2/15+2/35+2/63+2/99+2/143)$

$\Rightarrow \frac{1}{2} [(\frac{1}{3} - \frac{1}{5}) + (\frac{1}{5} - \frac{1}{7}) + (\frac{1}{7} - \frac{1}{9}) + (\frac{1}{9} - \frac{1}{11}) + (\frac{1}{11} - \frac{1}{13})]$ $rArr 1/2[(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)+(1/11-1/13)]$

$\Rightarrow \frac{1}{2} [\frac{1}{3} - \frac{1}{5} + \frac{1}{5} - \frac{1}{7} + \frac{1}{7} - \frac{1}{9} + \frac{1}{9} - \frac{1}{11} + \frac{1}{11} - \frac{1}{13}]$ $rArr 1/2[1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13]$

$\Rightarrow \frac{1}{2} [\frac{1}{3} - \frac{1}{13}]$ $rArr 1/2[1/3-1/13]$

$\Rightarrow \frac{1}{2} [\frac{13 - 3}{39}]$ $rArr 1/2[(13-3)/39]$

$\Rightarrow \frac{1}{2} . \frac{10}{39}$ $rArr 1/2. 10/39$

$\Rightarrow \frac{5}{39}$ $rArr 5/39$

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Simplify $\frac{1}{15} + \frac{1}{35} + \frac{1}{63} + \frac{1}{99} + \frac{1}{143}$ $1/15+1/35+1/63+1/99+1/143$ ?

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Simplify $\frac{1}{15} + \frac{1}{35} + \frac{1}{63} + \frac{1}{99} + \frac{1}{143}$ $1/15+1/35+1/63+1/99+1/143$ ?