Thread: Binomial problems (Urgent)

If (1+x)n = 1+C1x+C2x2+C3x3+……………………+Cnxn
1 ) Prove that: C0/1 - C1 /2 + C2/3 - ……………………………+ (-1)n Cn /(n+1) = 1/(n+1)
2) Prove that : C0/1 + C1 /2 + C2/3 + ……………………………+ Cn /(n+1) = {2(n+1) - 1}/(n+1)
3 ) Prove that : C1/ C0 + 2C2 / C1+ 3C3/ C2 +……………………………+ n .Cn / Cn -1 = n(n+1)/2

Most difficult task is writing the formula in LaTeX form :P



Q1 : integrate the function, so that every becomes
Then you just replace x by some particular value.

Q2 : similar trick

Q3 : I don't know; keep trying stuff like "derive" / "integrate" / "replace x by ..."