# Tricks

All posts tagged Tricks

## Descartes’ Rule of Signs explained by an IITian

This explanation of Descartes’ Rule of Signs was submitted by Ayush, a HashLearn tutor from IIT, Dhanbad.

Consider a polynomial equation p(x)=0 (descending powers of x)
i) Number of positive roots of the equation p(x)=0 cannot exceed the number of changes of sign in p(x).…

## Study Tips: Integral of sec(x).cosec(x)

This tip on integration was contributed by one of our top tutors, Shashwat.

Following up on our tips on calculus, this week we will explain the trick to finding the integral of the aforementioned function.

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## Study Tips: Differentiation of an Infinite Series

This tip on calculus was contributed by one of our top tutors, Shashwat.

What you will learn from this tip:
The trick to differentiate an infinite series.

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Consider the following question:
A function y is defined as

Find at x = 0.…

## Study Tips: Finding the Roots of Unity

This tip on roots of an equation, and complex numbers was contributed by one of our top tutors, Sudheer Naidu.

What you will learn from this tip:
• An understanding of the relation between complex numbers and the roots of unity.
• The trick to calculate the nth roots of unity.

## Study Tips: Sum of Infinite Telescoping Series

This tip on sequences and series was contributed by one of our top tutors, Rushil Shah.

What you will learn from this tip:
• An understanding of a telescoping series
• The trick to calculate the sum of a telescoping series

# Telescoping series

A telescoping series is any series where nearly every term cancels with a preceding or following term.…