Question

A = 1/15 + 1/35 + 1/63 +1/99 +...+1/9999

Answer 1

A=1/3x5+1/5x7+1/7x9+1/9x11+...+1/99x101

A=1/2x(1/3-1/5+1/5-1/7+1/7-1/9+...+1/99-1/101

A=1/2x(1/3-1/101)

A=1/2x(98/103)

A=49/103

Answer 2

  A = 1/3x5 + 1/5x7 + 1/7x9 + 1/9x11 +...+ 1/99x101

2A = 2/3x5 + 2/5x7 + 2/7x9 + 2/9x11 +...+ 2/99x101

2A = 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11 +....+ 1/93 - 1/97

2A = 1 - 1/97

2A = 96/97

 A = 96/97 : 2

A = 48/97

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Answer 3

A= 1/15 + 1/35 + 1/63 + 1/99 + ...+ 1/9999

A= 1/3*5 + 1/5*7 + 1/7*9 +...+ 1/99*101

A= 1/2 * ( 1/3 - 1/5 + 1/5 -1/7 + 1/7 - 1/9 + ...+ 1/99 - 1/101)

A= 1/2 * ( 1/3 - 1/101)

A= 1/2 * 98/103

A=  49/303