Show that the sum of n terms of the progression:

Question

logx, logx^2, log^3, logx^4...is
n(n+1/2)

Answer 1

logx^(n+1)

Proof:

Let S be the sum of n terms of the progression.

S = logx + logx^2 + logx^3 + ... + logx^n

Using the formula for the sum of a geometric progression,

S = logx * (1 + x + x^2 + ... + x^n-1)

S = logx * (x^n - 1) / (x - 1)

S = logx * (x^n - 1) / (x - 1)

S = n(n+1/2)logx^(n+1)

Therefore, the sum of n terms of the progression is n(n+1/2)logx^(n+1).

Answer 2

logx, logx^2, log^3, logx^4... for n terms
= logx + 2logx + 3logx + ... + nlogx
= logx (1 + 2 + ... + n)
= n(n+1)/2 * logx
or
log(x^(n(n+1)/2) )

Answer 3

HELP ME PLEASE
MS: Earth Science [M] (Sequential) (GP) Carroll / Earth's Land and Water / 05:Water in the Oceans
below passing
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the question 1 is Which is true when wave crests come closer together?

The wavelength is decreasing.
The wave is changing direction.
The frequency is decreasing.
The wave height is decreasing.
please help asap