Question

54. Find the sum of first n terms of :
(i) 4 + 44 + 444 +........
(ii) 0.7 + 0.77 + 0.777 +.........

55. Find the value of 0.423.

this is the two questions of highest mark

PLZZ solve this​

Answer 1

(i) 4+44+444+........

4/9 [9+99+999......n]

4/9 [(10-1) + (10^2-1) + (10^3-1) .....

(10^(n)-1]

4/9 [(10+10^2+10^3...) -n]

4/9 [ 10{10^(n)-1} - (10-1)-1]

4/81 [10{10^(n)-1} -1]

(ii) 0.7+0.77+0.777+......

7/10 + 7/100 + 7/1000.......

7 [1/10+1/100+1/1000....]

7 [ 1/10{1-1/10^n} / {1-(1/10)}

7[1/10{1-1/10^n} /9/10]

7[1-(1/10^n) /9]

question = 55.....

Find the value of 0.423.

423/1000

Answer 2

(i)4+44+444.....

=4+44+444+4444

(ii)0.7+0.77+0.777.....

=0.7+0.77+0.777+0.7777

55.0.423= 423/1000

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