Prove That 1+2+3++nnn+12

This Site Might Help You. 6/3 =2 =3+1/2 which is true. Take the first 3 of the numbers;.

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Can you prove that 1+2+3+.+n =n(n+1)/2?.

Prove that 1+2+3++nnn+12. Mozaffor Hussain Mozaffor, Assistant Teacher , BIAM Model school and college. Now say that it is true for a certain n. Upvote (0) Views (3008) Followers (0) Write an Answer Register now or log in to answer.

+ n = (n(n+1))/2 for n, n is a natural number Step 1:. Prove it is true for n+1, and this will prove it is true for any n. Prove 1 + 2 + 3 +.

If you want to prove it to yourself;. Question added by mohamed taha , مدرس , البشائر Date Posted:. 1 + 2 + 3 +.

+ n = (n(n+1))/2 Step. Epic Collection of Mathematical Induction :. (the given statement)\ Let P(n):.

Answer added by Md. Please show step by step. Educate the students.

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$\begin{array}{rcl} \zeta(-1)&=&\frac{1}{1-2^{2}}\sum_{n=0}^\infty\frac{1}{2^{n+1}}\sum_{k=0}^n{n\choose k}(-1)^{k}(k+1)\\[2mm] &=&-\frac{1}{3}\sum_{n=0}^1\frac{1}{2^{n+1}}\sum_{k=0}^n{n\choose k}(-1)^{k}(k+1)\\[2mm] &=&-\frac{1}{3}\cdot\frac{1}{2^{0+1}}{0\choose 0}(-1)^{0}(0+1)-\frac{1}{3}\cdot\frac{1}{2^{1+1}}{1\choose 0}(-1)^{0}(0+1)-\frac{1}{3}\cdot\frac{1}{2^{1+1}}{1\choose 1}(-1)^{1}(1+1)\\[2mm] &=&-\frac{1}{3}\cdot\frac{1}{2}\cdot1\cdot1\cdot1-\frac{1}{3}\cdot\frac{1}{4}\cdot1\cdot1\cdot1-\frac{1}{3}\cdot\frac{1}{4}\cdot1\cdot(-1)\cdot2\\[2mm] &=&-\frac{1}{6}-\frac{1}{12}+\frac{1}{6}\\[2mm] &=&-\frac{1}{12} \end{array}$

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