Question

Find the sum to n terms of the series 5+55+555

Answer 1

Answer:

615

Step-by-step explanation:

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Answer 2

first of all take 5 common like this

5(1+11+111+....n)

then multiply and divide by 9

5/9*9(1+11+111+....n)

5/9(9+99+999.....n)

now we can write 9 like this

5/9[(10-1)+(10*10-1)+(10*10*10-1).....n)

now

5/9(10+10*10+10*10*10....n)-[1+1+1+1....n)

so here a=10, r=10, r>1

so use this formulae

S=a(r to the power n - 1)/r-1

= 5/9[10(10 to the power n - 1)/10-1] - n

= 5/9[10/9(10 to the power n - 1) - n

= 50/81(10 to the power n -1) - 5/9n this is the answer have fun