Question

Number 56 please ..........

Answer 1

hey mate.
here's the solution
and here a should be 12

Answer 2

You Wonder-fool human =_+

$E(k) = \frac{1}{ \sqrt{k + 1} + \sqrt{k} } = ( \sqrt{k + 1} - \sqrt{k} )$

Now,

$\sum E(k) = \sum {}^{143}_4 ( \sqrt{k + 1 } - \sqrt{k} )$

$= > \sum E(k) = \sqrt{144} - \sqrt{4} = 10$

$= > \sum E(k) = 10 \equiv a - \sqrt{b}$

Clearly, comparing the Rational and Irrational Parts -> Only One option matches ✓✓

$a = 10 \\ \\ b = 0$
Answer - ( A )
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Note, answer can also be something like :

( 12 - √4 ) or ( 19 - √81 ) or something like that, so please take care when you're attending an irregular exam ^_^

Have fun day ( =_= better never ever forget this human )