5+55+555 n terms Change this term into G P then find the sum of this series - Maths - Sequences and Series

Question

5+55+555 n terms Change this term into G P then find the sum of
this series?

Ajinder Singh · Answer

5+55+555+ n
=5 (1+11+111+ n terms)
= 5 /9 (9+99+999+ nterms )
= 5/9 ( (10 -1 ) + (100-1) + (1000-1) + nterms )
= 5/9 [(10 +100 + 1000 + n terms (GP series ) ) - (1+1+1+1 n
terms )]
= 5/9 [ 10 ((10)n -1) / 10-1 ] - n ]
= 5/9 [ 10 (10n -1) /9 - n ]
= 5 /81 [ 10 (10n -1) - 9n ]

5+55+555...n terms. Change this term into G.P. then find the sum of this series?