Question

Find the sum upto n terms of the series 0.7+0.97+0.997+....

Answer 1

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Answer 2

Step-by-step explanation:

S n = 0.7 + 0.97 +...+

n

S n = (1 - 0.3) + (1 - 0.03) + (1 - 0.003) +...+n brmb.

S h =(1+1+...+n trmd)-( 0 * 3 + 0 * 3 + 0.003 +0...+ntems) 1*0 0*7

S n =h-( 3/10 + 3/100 + 3/1000 +...+56ms) 1.00 0.03 0.97

3/10 + 3/100 + 3/1000 +***+nkrms

becomes G. P with a = 3/10

1.8 0.003 997

r = l_{2}/t_{2} = beta/(10p) * (1p)/8 = 1/10 < 1

= 3 10 ( 1 - (1/10) ^ n 1 - 1/10

S_{n} = (a(1 - r ^ n))/(1 - r) aligned = 3 10 *(1- 1 10^ n ) 9 10 = 3 10 x 10 9 (1- 1 10^ n )\\ 9 10 = 1/3 * (1 - 1/(1 - n)) aligned

Final Answer!

S_{n} = n - 1/3 * (1 - 1/(10 ^ n))