JEE-Main - Grade 11 - Mathematics - Principle of Mathematical Induction - Importance and Snapshot of Principle of Mathematical Induction - Study ref# 611

Introduction:
Inductive reasoning depends on working with each case, and
developing a conjecture by observing the incidences till we observe each and
every case. Thus in simple words, the induction means the generalization from
particu... read more

JEE-Main - Grade 11 - Mathematics - Principle of Mathematical Induction - Importance and Snapshot of Principle of Mathematical Induction - Study ref# 612

Following sections must be covered to understand the
Principle of Mathematical Induction:
1. Motivation
2. The Principle of Mathematical Induction... read more

JEE-Main - Grade 11 - Mathematics - Principle of Mathematical Induction - Target Setup for Principle of Mathematical Induction - Study ref# 613

Student requires to achieve the following milestones to get better grip over Principal of Mathematical Induction. The milestones / targets are as follows:-Starting Point: Days 0Test TypeAppear on TestTarget TestsScorePractice Test000%... read more

JEE-Main - Grade 11 - Mathematics - Principle of Mathematical Induction - Study ref# 2452

Prove that by
using the principle of mathematical induction for all nN Answer: Let the given statement be P(n).
i.e., P(n):
Step 1. For n=1,
&nb... read more

JEE-Main - Grade 11 - Mathematics - Principle of Mathematical Induction - Study ref# 2453

Prove that by
using the principle of mathematical induction for all nN Answer: Let the given statement be P(n).
i.e., P(n):
i.e., P(n):
&nbs... read more

JEE-Main - Grade 11 - Mathematics - Principle of Mathematical Induction - Study ref# 2454

Prove that by
using the principle of mathematical induction for all nN Answer: Let the given statement be P(n).
i.e., P(n):
Step 1. For n=1,
P(1... read more

JEE-Main - Grade 11 - Mathematics - Principle of Mathematical Induction - Study ref# 2455

Prove that by
using the principle of mathematical induction for all nN Answer: Let the given statement be P(n).
i.e., P(n):
Step1.For n=1,
which is true.... read more

JEE-Main - Grade 11 - Mathematics - Principle of Mathematical Induction - Study ref# 2456

Prove that by
using the principle of mathematical induction for all nN Answer: Let the given statement be P(n).
i.e., P(n):
Step1. For n=1,P(1):
which... read more

JEE-Main - Grade 11 - Mathematics - Principle of Mathematical Induction - Study ref# 2457

Prove that by
using the principle of mathematical induction for all nN Answer: Let the statement be P(n).
i.e., P(n):
Step 1. For n=1,
... read more

JEE-Main - Grade 11 - Mathematics - Principle of Mathematical Induction - Study ref# 2458

Prove that by
using the principle of mathematical induction for all nN Answer: Let the given statement be P(n)
i.e., P(n):
Step1.For n=1,
i.e., P(1)= ,
which is true.
Step 2.L... read more

JEE-Main - Grade 11 - Mathematics - Principle of Mathematical Induction - Study ref# 2459

Prove that by
using the principle of mathematical induction for all nN Answer: Let the given statement be P(n)
i.e., P(n):
Step1.For n=1,
i.e., P(1)= ,
which is true.
Step 2.Let it is t... read more

JEE-Main - Grade 11 - Mathematics - Principle of Mathematical Induction - Study ref# 2460

Prove that by
using the principle of mathematical induction for all nN Answer: Let the given statement be P(n)
i.e., P(n):
Step1.For n=1,
&n... read more

JEE-Main - Grade 11 - Mathematics - Principle of Mathematical Induction - Study ref# 2461

Prove that by
using the principle of mathematical induction for all nN Answer: Let the given statement be P(n)
i.e., P(n):
Step1.For n=1,
&n... read more

JEE-Main - Grade 11 - Mathematics - Principle of Mathematical Induction - Study ref# 2462

Prove that is
divisible by 8 by using the principle of mathematical induction for all nN Answer: Let the given statement be P(n)
i.e., P(n): is
divisible by 8
Step1.For n=1,
i.e., P(1)#... read more

JEE-Main - Grade 11 - Mathematics - Principle of Mathematical Induction - Study ref# 2463

Prove that by
using the principle of mathematical induction for all nN Answer: Let the given statement be P(n).
i.e., P(n):
Step 1.For n=1,
i.e., P(1): 2×1+7<(1+3)2=9<16
which is true.
Step 2... read more

JEE-Main - Grade 11 - Mathematics - Principle of Mathematical Induction - Study ref# 2464

Prove that for all n∈N
.
by
using the principle of mathematical induction Answer: Let the given statement be P(n).
i.e., P(n):
&nbs... read more

JEE-Main - Grade 11 - Mathematics - Principle of Mathematical Induction - Study ref# 2465

Prove that
by
using the principle of mathematical induction for all n∈N . Answer: Let the given statement be P(n).
i.e., P(n):
Step 1.For n=1,
i.e., P(1):
Hence, it is true for n=1.
Step 2.Let it is true for n=... read more

JEE-Main - Grade 11 - Mathematics - Principle of Mathematical Induction - Study ref# 2466

Show that
is
a natural number for all n∈N. Answer: Let the given statement be P(n).
i.e., P(n): is
a natural number for all n∈N.
Step 1.For n=1,
i.e., P(1):
Hence, it is true for n=... read more