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Fri March 09, 2012 By:

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Sun March 11, 2012
we can see that Sk = a/(1-r) = 1/fact(k-1)
Now in the summation for k = 1 , 2 we get |(k2 - 3k + 1)Sk| = 1 + 1 = 2
For k = 3 to 100
We can write (k2 - 3k + 1)Sk = (k2 - 3k + 1)/fact(k-1) = {(k-1)(k-2) - 1}/fact(k-1) =
 1/fact(k-3) - 1/fact(k-1)
 
Now for k = 3 to 100
we get summation as { 1/fact(0) + 1/fact(1) + 1/fact(2) + .... 1/fact(97) } -
{ 1/fact(2) + 1/fact(3) + ...... + 1/fact(99) }
= 2 - { 1/fact(98) + 1/fact(99) } = 2 - 100/fact(99) = 2 - 100sq/fact(100)
When we add it to (100)sq/fact(100)   , we get Answer = 2
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