Home
Class 12
MATHS
If p is a prime, then sum of log(p)p^(...

If p is a prime, then sum of
`log_(p)p^(1//2)-log_(p)p^(1//3)+log_(p)p^(1//4)-……=`

A

`1+log2`

B

`1+log3`

C

`1-log2`

D

`2-log2 `

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Similar Questions

Explore conceptually related problems

Solve log_(8)(P^(2)-p)-log_(8)(p-1)=2

The value of N satisfying log_(a)[1+log_(b){1+log_(c)(1+log_(p)N)}]=0 is

P_(1), P_(2), P_(3) are altitudes of a triangle ABC from the vertices A, B, C and Delta is the area of the triangle, The value of P_(1)^(-1) + P_(2)^(-1) + P_(3)^(-1) is equal to-

If agt1,bgt1andcgt1 are in G.P., then show that 1/(1+log_(e)a),1/(1+log_(e)b)and1/(1+log_(e)c) are in H.P.

Given a right triangle ABC right angled at C and whose legs are given 1+4log_(p^2)(2p),1+2^(log_2(log_2(p)) and hypotenuse is given to be 1+log_2(4p) . The area of trianleABC and circle circumscribing it are Delta_1 and Delta_2 respectively.

Given a right triangle ABC right angled at C and whose legs are given 1+4log_(p^(2))(2p), 1+2^(log_(2)(log_(2)p)) and hypotenuse is given to be 1+log_(2)(4p) . The are of DeltaABC and circle circumscribing it are Delta_(1) and Delta_(2) respectively, then Q. Delta_(1)+(4Delta_(2))/(pi) is equal to :

If x = log p and y=(1)/(p), then

If x = log p and y=(1)/(p), then

If p >1 and q >1 are such that log(p+q)=logp+logq , then the value of log(p-1)+log(q-1) is equal to (a) 0 (b) 1 (c) 2 (d) none of these

If x,y,z are in G.P. (x,y,z gt 1) , then (1)/(2x+log_(e)x) , (1)/(4x+log_(e)y) , (1)/(6x+log_(ez)z) are in