Math Marvels: Binomial series: C1-(1+1/2)C2+(1+1/2+1/3)C3-...(1+1/2+1/3+..1/n)Cn=1/n

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Binomial Coefficient Properties SE7: Find (1+C1/C0)(1+C2/C1).....(1+Cn/Cn-1)? Binomial Coefficient Properties SE7: Find (1+C1/C0)(1+C2/C1).....(1+Cn/Cn-1)?
NEB Grade 12 Binomial theorem - C_1+2C_2+3C_3+..........+nCn = n2^(n-1) NEB Grade 12 Binomial theorem - C_1+2C_2+3C_3+..........+nCn = n2^(n-1)
C0 + C1 x/2 + C2 x²/3 + C3 x³/4 +....+ Cn xⁿ+¹/n+1 = (1+x)ⁿ+¹ – 1 / (n+1)x; using integration @EAG C0 + C1 x/2 + C2 x²/3 + C3 x³/4 +....+ Cn xⁿ+¹/n+1 = (1+x)ⁿ+¹ – 1 / (n+1)x; using integration @EAG
11.e) Prove that: C1/C0 + 2C2/C1 + 3C3/C2 +...+nCn/Cn-1=n(n+1)/2 If (1+x)ⁿ=C0+C1x+C2x²+...+Cnxⁿ. NEB 11.e) Prove that: C1/C0 + 2C2/C1 + 3C3/C2 +...+nCn/Cn-1=n(n+1)/2 If (1+x)ⁿ=C0+C1x+C2x²+...+Cnxⁿ. NEB
Show that (C0+C1)(C1+C2) ... (Cn-1 + Cn) = C1*C2 ... Cn*[(n+1) raised to power n] / n! Show that (C0+C1)(C1+C2) ... (Cn-1 + Cn) = C1*C2 ... Cn*[(n+1) raised to power n] / n!
Find value of C0 + 2*C1 + 3*C2 + ... + (n+1)*Cn. Find value of C0 + 2*C1 + 3*C2 + ... + (n+1)*Cn.
The Binomial Theorem : Fractional Powers : Expanding (1-2x)^1/3 The Binomial Theorem : Fractional Powers : Expanding (1-2x)^1/3
11.b) Prove that: C0+2C1+3C2+...+(n+1)Cn=(n+2).2^(n-1) If (1+x)ⁿ=C0+C1x+C2x²+...+Cnxⁿ. Binomial NEB 11.b) Prove that: C0+2C1+3C2+...+(n+1)Cn=(n+2).2^(n-1) If (1+x)ⁿ=C0+C1x+C2x²+...+Cnxⁿ. Binomial NEB