a boy take one or 2 steps at a time how he can climb a 10 steps
aashish kumar neelkhanti , 12 Years ago
Grade 11
Magical Mathematics[Interesting Approach]> permutation and combination...
1 Answers
Aman Bansal
Last Activity: 12 Years ago
Dear Aashish,
Let a be the number of ways to climb up a stairs of n steps with each time climbing 1 or 2 steps.
We are to compute
a .
To climb n steps, we may first climb 1 or 2 steps. In the former case, we are to climb n −1 more
steps, and this can be done in
a(n-1) ways. In the latter case, we are to climb n − 2 more steps, and this can be done in
a(n- 2) ways. Therefore, we obtain the recurrence relation
a(n).= a(n-1) + a(n-2)
Since the recurrence relation for
a(n) depends on two previous terms, we need two initial conditions.
We have
a (1)=1 and
a(2) = 2 . By direct computation, it is easy to obtain
a(10) = 89
We are to compute
a .
To climb n steps, we may first climb 1 or 2 steps. In the former case, we are to climb n −1 more
steps, and this can be done in
a(n-1) ways. In the latter case, we are to climb n − 2 more steps, and this can be done in
a(n- 2) ways. Therefore, we obtain the recurrence relation
a(n).= a(n-1) + a(n-2)
Since the recurrence relation for
a(n) depends on two previous terms, we need two initial conditions.
We have
a (1)=1 and
a(2) = 2 . By direct computation, it is easy to obtain
a(10) = 89
Best Of luck
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