\frac 1 12 %2B \frac 1 20 %2B \frac 1 30 %2B \

1.	\frac 1 12 %2B \frac 1 20 %2B \frac 1 30 %2B \frac 1 42 %2B \frac 1 56 %2B \frac 1 72 %2B \frac 1 90 %2B \frac 1 110 %2B \frac 1 132 %2B \frac 1 156 = ?
Answer» It can be written as 1/12 + 1/23 + 1/34 + 1/45 + 1/56 + 1/67 + 1/78 + /89 + 1/910 + 1/1011 + 1/1112 + 1/1213 It can be further expressed as 1/1 - 1/2 + 1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 + 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 – 1/12 + 1/12 - 1/13 Here all the terms get cancelled except the first and last one 1/1–1/13 12/13 Hence 12/13 is the answer Like my answer if you find it useful!

\frac 1 12 %2B \frac 1 20 %2B \frac 1 30 %2B \frac 1 42 %2B \frac 1 56 %2B \frac 1 72 %2B \frac 1 90 %2B \frac 1 110 %2B \frac 1 132 %2B \frac 1 156 = ?

Answer»

It can be written as 1/1*2 + 1/2*3 + 1/3*4 + 1/4*5 + 1/5*6 + 1/6*7 + 1/7*8 + /8*9 + 1/9*10 + 1/10*11 + 1/11*12 + 1/12*13

It can be further expressed as

1/1 - 1/2 + 1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 + 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 – 1/12 + 1/12 - 1/13

Here all the terms get cancelled except the first and last one

1/1–1/13

12/13

Hence 12/13 is the answer

Like my answer if you find it useful!