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Algebra Level 2

Calculate the sum of 1 2 ! + 2 3 ! + 3 4 ! + . . . . . . + 99 100 ! \frac { 1 }{ 2! } +\frac { 2 }{ 3! } +\frac { 3 }{ 4! } +......+\frac { 99 }{ 100! }

Assumptions

  • Take the value of 100! as 100 for the final calculation purpose.


The answer is 0.99.

Max B by Max B , 24, India

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1 solution

Max B
May 8, 2014

2 − 1 2 ! + 3 − 1 3 ! + . . . . . + 100 − 1 100 ! = ( 1 1 ! − 1 2 ! ) + ( 1 2 ! − 1 3 ! ) + . . . . . . . . . . + ( 1 99 ! − 1 100 ! ) = 1 − 1 100 ! n o w t a k e 100 ! a s 100 = 0.99 \frac { 2-1 }{ 2! } +\frac { 3-1 }{ 3! } +.....+\frac { 100-1 }{ 100! } \\ =\left( \frac { 1 }{ 1! } -\frac { 1 }{ 2! } \right) +\left( \frac { 1 }{ 2! } -\frac { 1 }{ 3! } \right) +..........+\left( \frac { 1 }{ 99! } -\frac { 1 }{ 100! } \right) \\ =1-\frac { 1 }{ 100! } \\ now\quad take\quad 100!\quad as\quad 100\\ =0.99\\

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who changed the title...calvin is it you ?????

Max B - 7 years, 1 month ago

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