Question

Show that the sum of n terms of the progression:
logx, logx^2, log^3, logx^4...is
n(n+1/2)

Answer 1

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 2

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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1.

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

Answer 3

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).