$40$.($\frac{171717}{303030}$+$\frac{171717}{424242}$+$\frac{171717}{565656}$)
$=$ $40$. ($\frac{171717:10101}{303030:10101}$+$\frac{171717:10101}{424242:10101}$+$\frac{171717:10101}{565656:101010}$)
$=$$40$.($\frac{17}{30}$+$\frac{17}{42}$+$\frac{17}{56}$)
$=$ $40$.[$17$.($\frac{1}{30}$+$\frac{1}{42}$+$\frac{1}{56}$)]
$=$ $40$ [$17$($\frac{1}{5.6}$+$\frac{1}{6.7}$+$\frac{1}{7.8}$)]
$=$ $40$ [$17$($\frac{1}{5}$ - $\frac{1}{6}$ + $\frac{1}{6}$ - $\frac{1}{7}$ + $\frac{1}{7}$ - $\frac{1}{8}$)
$=$ $40$ [$17$ . ($\frac{1}{5}$ - $\frac{1}{8}$)
$=$ $40$ [$17$ . $\frac{3}{40}$]
$=$ $40$ . $\frac{51}{40}$
$=$ $\frac{2040}{40}$=$51$
