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Help with the sum of the geometric sequence problem, Please!

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Could someone teach me how to do this?

thanks in advance!

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Using the natural logarithmic power rule, we know that if you have the logarithm of 2 raised to the r, then that just equals r times the logarithm of 2

ln(2r)= r*ln(2)

So, this just becomes an arithmetic series as the difference between any two terms will be ln(2):

ex.

5 * ln(2) - 4*ln(2) = ln(2)

So, you can use the arithmetic series formula to find this sum:

so, n=50 and u1 = 1*ln(2)   and u50= 50*ln(2)

S50= 50/2 * (ln(2) + 50*ln(2)) = 1275*ln(2)

 

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