mathematics
  Personalized »

KS3
 
 
 
Year 7
 
 
Year 8
 
 
Year 9

KS4
 
 
 
Year 10
 
 
Year 11

A-levels
 
 
 
Year 12 (AS)
 
 
Year 13 (A-levels)


physics
  Personalized »

 
 


KS4
 
 
 
KS4 Level Physics

A-levels
 
 
 
AS Level Physics
 
 
A-levels Physics


 
 
Private tutors
 
 
Find a tutor »


 


Unlock access to content
 
Select one option:



Free of charge
Unlock the chapter   "Sigma Notation for Sums of Series"  



Unlock access to the solution of problems in this chapter.
Free of charge Price: 3.00 £

Continue »
Subscribe to OpenProf     If you do not get a better grade, you get your money back!
 


Unlock access to all problems solutions.
Available from 8.25 £ / month.
Continue »
mathematics UK Year 10 Mathematics (KS4)
 
Solved problems for the chapter:
 

Sigma Notation for Sums of Series

download pdf
View the theory »
Mathematical induction
open
↓   Show theory [1]   ↓


Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:sigma_notation_for_sums_of_series/3604/


Example 1.

Calculate .

    
Example 2.

Calculate .

    
3.

Calculate .

    
4.

With mathematical induction, show that:


    
5.

With mathematical induction, show that:


    
6.

Using mathematical induction, show that:


    
7.

With mathematical induction, prove that the sum of the first n terms of the geometric sequence is equal to:


    
8.

Prove by induction that the sum of the first n terms of the arithmetic sequence is equal to:


    

9.

Calculate , find the formula for the sum of the given finite terms and prove that the formula is general by mathematical induction:


    
10.

Calculate , find the formula for the sum of the given finite terms and prove the correctness of the formula by mathematical induction:


    
11.

Calculate . Find the formula for the sum of the given series and prove the correctness and generality of the formula by complete induction:


    
12.

Calculate . Find the formula for the sum of the given finite series and prove the correctness and generality of the formula by mathematical induction:


    
13.

With mathematical induction prove:


, for each

   
14.

Prove by induction that the sum of the interior angles in a convex n-gon is equal to:


    
15.

Prove:


  • that the sum of four powers of 5, whose exponents are consecutive natural numbers, is divisible by 26.


  • by mathematical induction that for every natural number n.