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Tatiana [17]
3 years ago
8

Sum of series to n terms 0.4+0.44+0.444+....

Mathematics
1 answer:
svetoff [14.1K]3 years ago
8 0
0.4+0.44+0.444+\cdots=\dfrac4{10}+\dfrac{44}{100}+\dfrac{444}{1000}+\cdots=\displaystyle\sum_{k=1}^\infty\frac{\frac49(10^k-1)}{10^k}=\frac49\sum_{k=1}^\infty\left(1-\frac1{10^k}\right)

The nth partial sum is given by

S_n=\displaystyle\frac49\sum_{k=1}^n\left(1-\frac1{10^k}\right)
S_n\displaystyle=\frac49\bigg(\left(1-\frac1{10}\right)+\left(1-\frac1{100}\right)+\cdots+\left(1-\frac1{10^{n-1}}\right)+\left(1-\frac1{10^n}\right)\bigg)
S_n=\dfrac49\left(n-\dfrac{10^n-1}{9\times10^n}\right)=\dfrac4{81}(9n-1+10^{-n})

from which it follows that the infinite sum does not converge.
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3 0
2 years ago
Can you please help me with this! It's due in a couple hours.
castortr0y [4]

Answer:

f(2) = -5

Step-by-step explanation:

A point (x, y) lying on a function represents output value (y-value) of the function for any input value (x-value).

In other words y = f(x) for any input value of 'x'.  

From the graph attached,

For the input value x = 2,

Output value of the function is y = -5

Therefore, f(2) = -5 will be the answer.

5 0
3 years ago
I posted a question similar to this but I entered it wrong too many times :(
slava [35]

Answer:

\sqrt[4]{\frac{5}{7} }

Step-by-step explanation:

^4√5/^4√7

~Apply radical rules

^4√5/7

Best of Luck!

5 0
3 years ago
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Andrew [12]

The correct answer would be 11:32am. i hope this helps!

6 0
3 years ago
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dedylja [7]
963 would be rounded to become 1000.
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