Binomial coefficients in the denominator!
If the value of the sum
is then find the value of .
The answer is 1.00.
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1 solution
We have
S = r = 0 ∑ 1 0 0 6 ( r + 1 ) ( r + 1 2 0 1 3 ) 2 0 1 2 − 2 r
S = r = 0 ∑ 1 0 0 6 ( r + 1 ) ( r + 1 2 0 1 3 ) ( 2 0 1 3 − r ) − ( r + 1 )
S = r = 0 ∑ 1 0 0 6 ( r + 1 ) ( r + 1 2 0 1 3 ) 2 0 1 3 − r − ( r + 1 2 0 1 3 ) 1
S = r = 0 ∑ 1 0 0 6 ( r 2 0 1 3 ) 1 − ( r + 1 2 0 1 3 ) 1
This is a telescopic series.Thus
S = 1 − ( 1 0 0 7 2 0 1 3 ) 1
Thus the required answer is 1 − ( 1 0 0 7 2 0 1 3 ) 1 + ( 1 0 0 6 2 0 1 3 ) 1 = 1