What is the NO-SHORTCUT approach for learning great Mathematics?

# How to Pursue Mathematics after High School?

For Students who are passionate for Mathematics and want to pursue it for higher studies in India and abroad.

Try this beautiful problem from the PRMO II, 2019 based on Missing Integers.

## Missing Integers - PRMO II 2019

Consider the sequence of numbers [n+$\sqrt{2n}+\frac{1}{2}$] for $n \geq 1$, where [x] denotes the greatest integer not exceeding x. If the missing integers in the sequence are $n_1<n_2<n_3<...$ then find $n_{12}$.

• is 107
• is 78
• is 840
• cannot be determined from the given information

### Key Concepts

Real Numbers

Algebra

Integers

PRMO II, 2019, Question 1

Elementary Algebra by Hall and Knight

## Try with Hints

First hint

$[n+\sqrt{2n}+\frac{1}{2}]$=[$(\sqrt{n}+\frac{1}{\sqrt{2}})^2$]

Let P=[$(\sqrt{n}+0.7)^2$]

Second Hint

given $n \geq 1$, put n=1 gives P=2

n=2 gives P=4

n=3 gives P=5

n=4 gives P=7

n-5 gives P=8

n=6 gives P=9

n=7 gives P=11

Final Step

here missing number are

1,3,6,10,... which is following a certain pattern

1, 1+2, 3+3, 6+4, 10+5, 15+6, 21+7, 28+8, 36+9, 45+10, 55+11, 66+12.

so, $n_{12}$=78.

## What to do to shape your Career in Mathematics after 12th?

From the video below, let's learn from Dr. Ashani Dasgupta (a Ph.D. in Mathematics from the University of Milwaukee-Wisconsin and Founder-Faculty of Cheenta) how you can shape your career in Mathematics and pursue it after 12th in India and Abroad. These are some of the key questions that we are discussing here:

• What are some of the best colleges for Mathematics that you can aim to apply for after high school?
• How can you strategically opt for less known colleges and prepare yourself for the best universities in India or Abroad for your Masters or Ph.D. Programs?
• What are the best universities for MS, MMath, and Ph.D. Programs in India?
• What topics in Mathematics are really needed to crack some great Masters or Ph.D. level entrances?
• How can you pursue a Ph.D. in Mathematics outside India?
• What are the 5 ways Cheenta can help you to pursue Higher Mathematics in India and abroad?

## Want to Explore Advanced Mathematics at Cheenta?

Cheenta has taken an initiative of helping College and High School Passout Students with its "Open Seminars" and "Open for all Math Camps". These events are extremely useful for students who are really passionate for Mathematic and want to pursue their career in it.

To Explore and Experience Advanced Mathematics at Cheenta

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