Simplify 1/15+1/35+1/63+1/99+1/143?

2 Answers
Oct 27, 2017

1/15+1/35+1/63+1/99+1/143=5/39

Explanation:

1/15+1/35+1/63+1/99+1/143

= 1/(3xx5)+1/(5xx7)+1/(7xx9)+1/(9xx11)+1/(11xx13)

= (7xx9xx11xx13+3xx9xx11xx13+3xx5xx11xx13+3xx5xx7xx13+3xx5xx7xx9)/(3xx5xx7xx9xx11xx13)

= (9009+3861+2145+1365+945)/135135

= 17325/135135

= 3465/27027 - dividing by 5

= 385/3003 - dividing ny 9

= 35/273 - dividing by 11

= 5/39 - dividing by 7

Oct 27, 2017

5/39

Explanation:

Given, 1/15+1/35+1/63+1/99+1/143

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

rArr 2/2(1/15+1/35+1/63+1/99+1/143)

rArr 1/2(2/15+2/35+2/63+2/99+2/143)

rArr 1/2[(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)+(1/11-1/13)]

rArr 1/2[1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13]

rArr 1/2[1/3-1/13]

rArr 1/2[(13-3)/39]

rArr 1/2. 10/39

rArr 5/39