7/36=(3+4)/(4*9)= 1/ 12+ 1/9

29/56=(2 1+8)/(7*8)=3/8+ 1/7

37/63=(28+9)/(7*9)=4/9+ 1/7

4 1/72=(32+9)/(8*9)=4/9+ 1/8

53/77=(42+ 1 1)/(7* 1 1)=6/ 1 1+ 1/7

29/84=(36-7)/(7* 12)=3/7- 1/ 12

3/88=( 1 1-8)/(8* 1 1)= 1/8- 1/ 1 1

So Tonga is

1/7+3/8+ 1/ 12+ 1/9+3/8+ 1/7+4/9+ 1/7+4/9+ 1/8+6/ 1 1+ 1/7+3/7- 1/ / kloc-0/2+ 1/8- 1/ 1 1= 1+ 1+ 1+5/ 1 1=38/ 1 1

Is it like this:

39* 148/ 149+ 148*86/ 149+48*74/ 149

=(39* 148+86* 148+24*2*74)/ 149

=(39+86+24)* 148/ 149

= 149* 148/ 149

= 148

( 1- 1/2*2)*( 1- 1/3*3)*```````*( 1- 1/ 10* 10)

( 1- 1/2^2)=( 1- 1/2)( 1+ 1/2)= 1/2*3/2

( 1- 1/3^2)=( 1- 1/3)( 1+ 1/3)=2/3*4/3

...

( 1- 1/9^2)=8/9* 10/9

( 1- 1/ 10^2)=9/ 10* 1 1/ 10

( 1- 1/2^2)( 1- 1/3^2)( 1- 1/4^2)...( 1- 1/9^2)( 1- 1/ 10^2)

= 1/2*3/2*2/3*4/3*...*8/9* 10/9*9/ 10* 1 1/ 10

= 1/2* 1 1/ 10

= 1 1/20

1/( 1+2)+ 1/( 1+2+3)+ 1/( 1+2+3+4)+…+ 1/( 1+2+3+…+49)+ 1/( 1+2+3+…+50)

= 1/[( 1+2)*2/2]+ 1/[( 1+3)*3/2]+ 1/[( 1+4)*4/2]+……+ 1/[( 1+50)*50/2]

=2/(2*3)+2/(3*4)+2/4*5+……+2/( 100*99)

=[ 1/2*3+ 1/3*4+ 1/4*5+......+ 1/50*5 1]*2

=( 1/2- 1/3+ 1/3- 1/4+ 1/4- 1/5+……+ 1/50- 1/5 1)*2

=( 1/2- 1/5 1)*2

=49/ 102*2

=49/5 1