principle of mathematical induction
TRANSCRIPT
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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
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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
....
....
....
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N.)P( Induction alMathematicof Principle using by Hence true. is )P( whenever true is )1P(
R.H.S2
11 1
nn
kk
k
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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
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k
kk
kn
n
n
n
nn
......
,
......
,
,
.......
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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
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k
kkk
k
kkkk
)(
))((
.......