# Numerical Analysis-Summation Formula (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 1 - 3 of 3

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## Question number: 1

» Numerical Analysis » Summation Formula » Euler-Maclaurin's

Appeared in Year: 2015

### Describe in Detail

By using Euler-Maclaurin formula, find the sum

### Explanation

The Euler-Maclaurin formula is

where

Given the equation

## Question number: 2

» Numerical Analysis » Summation Formula » Euler-Maclaurin's

Appeared in Year: 2014

### Describe in Detail

Using Euler’s method, compute the values of y correct upto 4 places of decimal for the differential equation with initial condition x _{0} = 0, y _{0} = 1, taking h = 0.05.

### Explanation

The given differential equation is

with initial condition x _{0} = 0, y _{0} = 1, taking h = 0.05.

Using Euler’s method,

where

So, putting the initial condition, when n = 0

and

Now first modification of y _{1}

## Question number: 3

» Numerical Analysis » Summation Formula » Euler-Maclaurin's

Appeared in Year: 2013

### Describe in Detail

Solve the equation:

Use Euler algorithm and tabulate the solution at x = 0.1, 0.2, 0.3.

### Explanation

The given differential equation is

with initial condition x _{0} = 0, y _{0} = 0

Using Euler, s method,

where

We obtain y at x = 0.1

Again obtain y at x = 0.2

Similarly y at x = 0.3