Series problem - 11th Dec'15

Question

If !!f(k) = (5 + k^2 - (k+1)^2)/2!!

Then !!f(1) + f(2) + .................. + f(10) = ?!!

!!a)-30!!

!!b)-35!!

Solution

In the given equation !!f(k) = (5 + k^2 - (k+1)^2)/2!!

!!=> f(k) = (5 + k^2 - k^2 - 1 - 2k)/2!!

!!=> f(k) = (4 - 2k)/2!!

!!=> f(k) = 2 - k!!

Putting !!k = 1!! in this equation, we get

!!f(1) = 2 - 1!!

Similarly, !!f(2) = 2 - 2!!

and !!f(10) = 2 - 10!!

Hence, !!f(1) + f(2) + .................. + f(10) = (2xx10) - (1 + 2 + ............ + 10)!!

!!= 20 - (10xx11)/2!!

!!= 20 - 55!!

!!= -35!!

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