+ ... + 



Prove using induction, that the above is equal to





Base case:

S(1) = 5



and 









Hypothesis:

Assume 

   (*)

holds for n=k.





Now let n=k+1:





Re-writing the S(k) term using (*):

 + 



Now re-arrange (step-by-step shown):













add and subtract 





finally:





Thus (*) is true for n=k+1



 

RELATED QUESTIONS

use the principals of mathematical induction to prove the following statement... (answered by greenestamps)

Use mathematical induction to prove the following:
For each natural number... (answered by Edwin McCravy,amalm06)

use the principals of mathematical induction to prove the following statement... (answered by math_helper)

Prove by mathematical induction
1^2+3^2+5^2+.......upto n terms =... (answered by rothauserc)

Mathematical Induction Sum

Use mathematical induction to prove:
3/1*2*2 + 4/2*3*2^2 +  (answered by Edwin McCravy)

prove that the sum of all natural numbers divisible by 5 is equal to 5n(n+1)/2 using... (answered by Edwin McCravy)

Hello, this is a mathematical induction question i had a hard time to prove

Show that,  (answered by math_helper)

use mathematical induction to prove that the statement is true for all positive integers.  (answered by t0hierry,greenestamps)

Mathematical induction


How can we prove that :
(1 + 1 / 3) (1 + 5 / 4)(1 + 7 /... (answered by ikleyn)