Q. For n=1,2,3,4....
, Xn = 1/5(n+3)(n+4) then what is the value
of 1/X1 + 1/X2 +.. +1/X996 ?
Answers
Given : For n=1,2,3,4....
Xₙ = (1/5) (n + 3) (n + 4)
To Find : 1/X₁ + 1/X₂ +.. +1/X₉₉₆
Solution:
1/X₁ = 5/{ (1 + 3) (1 + 4) } = 5/(4 * 5)
1/X₂ = 5/{ (2 + 3) (2 + 4) } = 5/(5 * 6)
1/X₉₉₆ = 5/{ (999 + 3) (999 + 4) } = 5/(999 * 100)
1/X₁ + 1/X₂ +.. +1/X₉₉₆
= 5/(4 * 5) + 5/(5 * 6) + __________+ 5/(999 * 100)
= 5 ( 1/(4 * 5) + 1/(5 * 6) + _______________1/(999*100))
= 5 ( (1/4 - 1/5) + (1/5 - 1/6) + ________+(1/998 - 1/999) +( 1/999 - 1/1000))
=5 ( 1/4 - 1/1000)
= 5( 996/1000)
= 4980/1000
= 498/100
= 4.98
1/X₁ + 1/X₂ +.. +1/X₉₉₆ = 4.98
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