n=1:     Ok for n=1.  This is the base-case. 



Assume it is true for n=k:  that is,   + ... +  =   holds for n=k.   This is the hypothesis statement.



Now look at the case n=k+1:



 + ... +  



If we exclude the very last term for a second, the remainder is the same case as n=k, which we can re-write by applying the hypothesis:



=  + 



Putting everthing over a common denominator (step-by-step):

= 



= 



= 



Dividing the numerator by the denominator:

=    DONE (the hypothesis leads to truth for n=k+1)







 

RELATED QUESTIONS

Prove by mathematical induction

{{{1/(1*2) + 1/(2*3) + 1/(3*4)}}}+ ...+{{{1/n(n+1) =... (answered by Edwin McCravy)

please help me with prove of mathematical induction of this question 1+r+r^2+r^3+....+r^n  (answered by math_helper)

Use mathematical induction to prove that:... (answered by stanbon,ikleyn)

please help me with this
use the method of mathematical induction to prove the following
 (answered by math-vortex)

USE PRINCIPLE OF MATHEMATICAL INDUCTION TO PROVE THE FORMULA
1(1!) + 2(2!) + 3(3!)... (answered by Edwin McCravy)

Use mathematical induction to prove the following. 

N^3 < or = (N+1)^2 ; N> or =... (answered by ikleyn)

Prove by mathematical induction: ∑_(i=1)^n (3^i= 3(3^n-1)/2)   (answered by Edwin McCravy)

Induction Sum:
Prove using mathematical induction that:

1/1*2*3 + 1/2*3*4 + 1/3*4*5... (answered by robertb)

Hello, 
could I please have some help with this question,

Prove by mathematical... (answered by KMST)