Question

0.7+0.77+0.777..........+ n terms =​

Answer 1

Hlew,

Here's your answer....

Sum = 0.7 + 0.77 + 0.777 + …. up to n terms

= 7/9(0.9 + 0.99 + 0.999 + … up to n terms)

= 7/9[(1 – 0.1) + (1 – 0.01) + (1-0.001) + … up to n terms]

= 7/9[(1 + 1 + 1… upto n terms) – (1/10 + 1/100 + 1/1000 + … upto n terms)]

= 7/9[n – 0.1 * (1 – (0.1)^n)/(1 – 0.1)]

= 7/81[9n – 1 + 10^-n]

Thanks.

Sorry baby 'wink'

Answer 2

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= 0.7 + 0.77 + 0.777 + ........ + n terms

= 7/10 + 77/100 + 777/1000 + .......

Multiplying by 1/9 and talking 7 common we get,

= 7/9 ( 9/10 + 99/100 + 999/1000 + .....

Now, after simplifying we get the answer as ,

= 7/81 (9n -1 + 10^-n)