Problem Based on Multiplication Formula Part 1

1). Problem of 1/19

1/19 = 10^(-1) (1/(1 + 1)) + 10^(-2) (1/(1 + 1)^2) + 10^(-3) (1/(1 + 1)^3) + .....

= 10^(-1) * (1/2) + 10^(-2) * (1/2)^2 +10^(-3) * (1/2)^3 + ........

= 10^(-1) * (0.50) + 10^(-2) * (0.25) +10^(-3) * (0.125) + ........

= 0.05 + 0.0025 + 0.000125 + 0.00000625 + .......

= 0.052631.....

2). Find 1/39 by ekadhikena process.

Now ekadhikena purva is 3 + 1 = 4

1/39 = ........................................1

= ......................................41

= ....................................641

= ..................................5641

= ................................25641

= ..............................025641

This is to be continue to obtain result .

3). Find 1/49 by ekadhikena process.

Now ekadhikena purva is 4 + 1 = 5

1/49 = ........................................1

= ......................................51

= ....................................551

= ..................................7551

= ................................77551

= ..............................877551

Denominator - Numerator = 49 -1 = 48 is obtained as 5*9 + 3

Hence half of the process completed.

This is to be continue to obtain result .

Milan Tomic

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