## MYTUTOR SUBJECT ANSWERS

682 views

### Prove that sum(k) from 0 to n is n(n+1)/2, by induction

Proof by induction involves making an assumption, and using that assumption to prove that the consecutive case follows the pattern.

The key to this is realising that most questions follow the same structure, usually involving rearranging algebra. Remember to try to see where you can use the induction step, and how you can rearrange it to make it clear how the induction step fits in. Just keep calm, write out every step carefully, and the answers will follow.

Base case: for k=1, sum(0+1) = 1 and 1(1+1)/2 = 1, and we have shown that the claim is true in this case.

Hypothesis: suppose the claim is true for k=n

Induction step: for k=n+1 , take the sum:

sum(k) [0--n+1] = sum(k)[0--n] + n+1 = n(n+1)/2 +n+1 = (n2+n)/2 + (2n+2)/2 = (n2+3n+2)/2

= (n+1)(n+2)/2 and we have shown the claim

Conclusion: As the claim is true for 0 and 1, and we have shown it to be true if it is true for n=k, by induction we have proved it true for all n in the natural numbers.

2 years ago

Answered by Nadine, an A Level Further Mathematics tutor with MyTutor

## Still stuck? Get one-to-one help from a personally interviewed subject specialist

#### 122 SUBJECT SPECIALISTS

£20 /hr

Degree: Mechanical Engineering (Masters) - Manchester University

Subjects offered:Further Mathematics , Physics+ 2 more

Further Mathematics
Physics
Maths
.PAT.

“"It is the supreme art of the teacher to awaken joy in creative expression and knowledge." Albert Einstein”

MyTutor guarantee

£30 /hr

Degree: Physics (Bachelors) - Oxford, St Peter's College University

Subjects offered:Further Mathematics , Physics+ 2 more

Further Mathematics
Physics
Maths
.PAT.

“Studying Physics at the University of Oxford. Looking to tutor maths and physics at all levels, be sure to send me a message if you have any questions!”

£30 /hr

Degree: MMathPhil Mathematics and Philosophy (Bachelors) - Oxford, St Anne's College University

Subjects offered:Further Mathematics , Maths+ 3 more

Further Mathematics
Maths
.MAT.
-Personal Statements-
-Oxbridge Preparation-

“University of Oxford Maths and Philosophy student happy to help students learn and stay motivated!”

#### About the author

£20 /hr

Degree: Mathematics (Bachelors) - Warwick University

Subjects offered:Further Mathematics , Science+ 3 more

Further Mathematics
Science
Physics
Maths
Chemistry

MyTutor guarantee

### You may also like...

#### Other A Level Further Mathematics questions

If a car of mass 1000kg travels up a slope inclined at 5 degrees at a speed of 20 meters per second calculate the power output of the car's engine (assuming a resistive force due to friction of 500N)

How do I sketch the locus of |z - 5-3i | = 3 on an Argand Diagram?

Find the displacement function if the acceleration function is a=2t+5. Assume a zero initial condition of displacement and v=8 when t=1.

Prove that sum(k) from 0 to n is n(n+1)/2, by induction

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this.