Simplify 1/15+1/35+1/63+1/99+1/143115+135+163+199+1143?

2 Answers
Oct 27, 2017

1/15+1/35+1/63+1/99+1/143=5/39115+135+163+199+1143=539

Explanation:

1/15+1/35+1/63+1/99+1/143115+135+163+199+1143

= 1/(3xx5)+1/(5xx7)+1/(7xx9)+1/(9xx11)+1/(11xx13)13×5+15×7+17×9+19×11+111×13

= (7xx9xx11xx13+3xx9xx11xx13+3xx5xx11xx13+3xx5xx7xx13+3xx5xx7xx9)/(3xx5xx7xx9xx11xx13)7×9×11×13+3×9×11×13+3×5×11×13+3×5×7×13+3×5×7×93×5×7×9×11×13

= (9009+3861+2145+1365+945)/1351359009+3861+2145+1365+945135135

= 17325/13513517325135135

= 3465/27027346527027 - dividing by 55

= 385/30033853003 - dividing ny 99

= 35/27335273 - dividing by 1111

= 5/39539 - dividing by 77

Oct 27, 2017

5/39

Explanation:

Given, 1/15+1/35+1/63+1/99+1/143115+135+163+199+1143

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)22(115+135+163+199+1143)

rArr 1/2(2/15+2/35+2/63+2/99+2/143)12(215+235+263+299+2143)

rArr 1/2[(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)+(1/11-1/13)]12[(1315)+(1517)+(1719)+(19111)+(111113)]

rArr 1/2[1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13]12[1315+1517+1719+19111+111113]

rArr 1/2[1/3-1/13]12[13113]

rArr 1/2[(13-3)/39]12[13339]

rArr 1/2. 10/3912.1039

rArr 5/39539