Chapter 12: Q. 1 (page 830)

use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.
2+4+6+....+2n=n(n+1)

Short Answer

Expert verified

We proves that the statement is true using the mathematical induction

Step by step solution

Given information

We are given a sequence

2+4+6+....+2n=n(n+1)

We check for n=1

LHS= 2

RHS=1(1+1)

hence LHS=RHS

Hence the statement is true for n=1

Assume the statement to be true for n

We get,

$2 + 4 + 6 + . . . . + 2 n = n (n + 1)$

Now we prove that the statement is true for n+1

That is we have to prove that

$2 + 4 + 6 + . . . + 2 n + 2 (n + 1) = (n + 1) (n + 2)$

Consider the left hand side

We have,

$2 + 4 + 6 + . . . . + 2 n + 2 (n + 1) = n (n + 1) + 2 (n + 1) = (n + 1) (n + 2) = R H S$

Hence proved the statement is true for all n belonging to natural numbers

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use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.
2+4+6+....+2n=n(n+1)

Short Answer

Step by step solution

Given information

We check for n=1

Assume the statement to be true for n

Now we prove that the statement is true for n+1

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Most popular questions from this chapter

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use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.2+4+6+....+2n=n(n+1)

Short Answer

Step by step solution

Given information

We check for n=1

Assume the statement to be true for n

Now we prove that the statement is true for n+1

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Calculus

Applied Mathematics

Probability and Statistics

Mechanics Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers n.
2+4+6+....+2n=n(n+1)