Find the sum to n terms of the sequence 5+55+555... to n terms

1.	Find the sum to n terms of the sequence 5+55+555... to n terms
Answer» Answer : 5+ 55+555+......n term5(1+11+111+........n term)Dividing and multliply by 9 5/9(9+99+999.....n term)5/9{(10-1)+(100-1)+1000-1)... n term}5/9{(10+10²+10³+... n term)-(1+1+1+...n term)}5/9[{10(10n-1)/10-1)}-n]5/81{10(10n-1)-n<br>Answer:\xa0Sum = 5 + 55 + 555 + …. n terms.= 5/9 [9 + 99 + 999 + …. n terms]= 5/9 [(10 – 1) + (100 – 1) + (1000 – 1) + … n terms]= 5/9 [10 + 100 + 1000 ….. – (1 + 1 + … 1)]= 5/9 [10(10n\xa0– 1)/(10 – 1) + (1 + 1 + … n times)]= 50/81(10n\xa0– 1) – 5n/9

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