Question

Q 10.1

Answer 1

Required sum = 4 + 44 + 444 +........... upto n terms
= 4(1 + 11 + 111 +........... upto n terms)
=`4/9`(9 + 99 + 999 +........... upto n terms)

=`4/9`[(10 - 1) + (100 - 1) + (1000 - 1) +........... upto n terms)

=`4/9`[(10 + 10² + 10³ +........... upto n terms)-(1 + 1 + 1 +........... upto n terms)]

=`4/9[(10(10^n-1))/(10-1)-n]`

=`4/9[10/9(10^n-1)-n]`