Question

find the sum to n term 8+88+888+_ _ _ _​

Answer 1

Answer:

8888

Step-by-step explanation:

Answer 2

Answer:

8/9 {10(10^n-1)/9} - n

Step-by-step explanation:

8+88+888+8888+88888 .................................n

Taking 8 as common

8(1+11+111+1111+11111+....................................................................n)

Multiply and divide by 9

8/9 (9+99+999+9999+99999+.............................n)

8/9 {(10-1)+(100-1)+(1000-1)+(10000-1)+(10000-1)...............................................n}

8/9 {(10+100+1000+10000+100000)-(1+1+1+1+1................n)}

(10+100+1000+10000+100000) is a GP

a=10 , r = 100/10 = 10

When r>1

Sn = a (r^n - 1) / (r-1)

Sn= 10 (10^n - 1) / (10-1)

Sn = 10(10^n - 1) / 9

Now replacing the value

8/9 {10(10^n-1)/9} - n

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