$1/30 + 1/42 + 1/56 + 1/72 + 1/90 + 1/110$ = ? Options: A . &nbsp$6/55$ B . &nbsp$√{2}2/27$ C . &nbsp$5/27$ D . &nbsp$1/9$

$1/30 + 1/42 + 1/56 + 1/72 + 1/90 + 1/110$ = ?

Question

$1/30 + 1/42 + 1/56 + 1/72 + 1/90 + 1/110$ = ?

Options:

A . $6/55$

B . $√{2}2/27$

C . $5/27$

D . $1/9$

Answer: Option A
Answer: (a)Using Rule 2,$1/{5×6} + 1/{6×7} + 1/{7×8} + 1/{8×9} + 1/{9×10} + 1/{10×11}$= $1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8 + 1/8 - 1/9 +1/9 - 1/10 +1/10 - 1/11 +1/11$= $1/5 - 1/11 ={11 - 5}/55 = 6/55$

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