Find the sum of the series 4 +44 +444 +4444 + ...
to n terms.
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Step-by-step explanation:
Sn=4+44+444+4444+.........n term
=4(1+11+111+1111+...........n)
=4/9(9+99+999+9999+.......n)
=4/9{(10-1)+(10²-1)+(10³-1)+.......n)
=4/9{(10+10²+10³+.....n)-(1+1+1+.....n)
=4/9[{10(10^n-1)}/(10-1)-n]
=4/9[{10(10^n-1)}/9-n]