BY- RITESH KUMAR

CLASS- XI SCIENCE

ROLL NO- 16

TOPIC- PRINCIPLE OF MAHEMATICAL

INDUCTION.

INCLUDES- Q.9 & 10 (EX-4.1)

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,

)(

,

....

1.... 21

121

81

41

21

for true is result the Suppose true. is 1P

1 for true is Result 21

21

1R.H.S

21

L.H.S

1 For21

121

81

41

21

:Q.9

kk

nn

kn

n

n

21

21

1

21

121

1

(1)] [From .... 2

121

1

21

21

81

41

21

21

81

41

21

L.H.S Consider2

11

21

81

41

21

1 for it prove shall We

1

1

1

11

k

k

kk

kk

k

kk

kn

....

....

....

N.)P( Induction alMathematicof Principle using by Hence true. is )P( whenever true is )1P(

R.H.S2

11 1

nn

kk

k

1061

53131

1181

851

521

1 for result the prove shall We

....{1} 462313

11181

851

521

then,

for true is result the Supposetrue. is P(1)

R.H.SL.H.S 101

461

R.H.S

101

521

L.H.S

1 For:SOLUTION

4623131

1181

851

521

:Q.10

k

k

kk

kn

k

k

kk

kn

n

n

n

nn

......

,

......

,

,

.......

N. true is )P( Induction alMathematicof Principle using By true. is )P( whenever true is )1P(

R.H.S1061

106123

231

106253

231

531

2231

53231

46

53231

23131

1181

851

521

L.H.S Consider

2

nn

kk

k

k

k

kk

k

k

kk

k

k

k

k

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k

kkkk

)(

))((

.......