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Mathematics Forum

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shin

I Need your help please...everybody!!
replied on: 4/4/2005 2:33:28 AM

Triangle formulae:

for N=1 it is 1
for N=2 it is 1+2
for N=3 it is 1+2+3

so,for some N=N it is 1+2+3+.....+n

using sum to arithematic progresion it is,
=N/2(2*1+(N-1)*1)
=1/2(N)(N+1).

Pascal triangle:

Hope you know binomial theorem,

for n=2 it is 1C0=1
for n=3 it is 2C0+2C1+2C2=4

so on obsevation for n=N it is sum of r=0 to r=n (N-1)C(r-1) = 2^(N-1)

to get that put x=1 in expansion of (x+1)^(N-1).

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