Question

Find the sum of the first n terms of 4+44+444+....

Answer 1

=4(1+11+111+1111+−−−−−−nterms)

=49(9+99+999+−−−−−−−−−−−nterms)

=49(10−1+100−1+1000−1+−−−−−−−−−−−nterms)

=49((10−1)+(102−1)+(103−1)+−−−−−−−−−−−nterms)

=49[10+102+103+−−−−−−−−−−−nterms−n]

=49[10(10n−1)10−1−n]

=49[10(10n−1)9−n].