Question

h.c.f of 0.2,0.22,0.222​

Answer 1

Step-by-step explanation:

This can be solved using geometric progression:

0.2 + 0.22 + 0.222 + 0.2222 + ….

2(0.1 + 0.11 + 0.111 + 0.1111 + ….)

2/9 ( 0.9 + 0.99 + 0.999 + 0.9999 + ….)

2/9 ( ( 1 - 0.1 ) + ( 1 - 0.01 ) + ( 1 - 0.001 ) + ( 1 - 0.0001 ) + …. )

2/9 ( 1 - 0.1 + 1 - 0.01 + 1 - 0.001 + 1 - 0.0001 + ….)

2/9 ( (1 + 1 + 1 + 1 + ….) - ( 0.1 + 0.01 + 0.001 + 0.0001 + ….))

2/9 ( n - ( 0.1 + 0.01 + 0.001 + 0.0001 + ….))

2/9 ( n - (( 0.1 ( 1 - 0.1^n)/( 1 - 0.1))))

2/9 ( n - (( 0.1 / 0.9)( 1 - 0.1^n)))

2/9 ( n - (1/9)(1 - 0.1^n))

This is the general formula to find sun of n series: 0.2 + 0.22 + 0.222 + …