Series into sigma notation

2,528

$$\sum_{k=1}^{51}(-1)^k(2k-1)$$

Share:
2,528

Related videos on Youtube

Sumeet
Author by

Sumeet

Updated on September 18, 2022

Comments

  • Sumeet
    Sumeet about 1 year

    How do I convert $-1 + 3 - 5 +...- 101$ into sigma notation.

    I tried to divide the series into $-1 -5 -7 -...$ and $3+7+9$ but i'm not too sure if that is correct.

    • Claude Leibovici
      Claude Leibovici about 6 years
      Think that they are odd numbers and about $(-1)^n$.
  • Sumeet
    Sumeet about 6 years
    Yes that is the answer, but i don't get where it comes from?
  • Michael Rozenberg
    Michael Rozenberg about 6 years
    @Sumeet Singh $(-1)^k$ gives changing of signs. $2k-1$ it's $a_k$ in the arithmetic progression. $a_1=1$ and $d=2$. $a_k=a_1+(k-1)d.$
  • Sumeet
    Sumeet about 6 years
    Oh that makes sense now. Thank you very much
  • Michael Rozenberg
    Michael Rozenberg about 6 years
    @Sumeet Singh You are welcome!
  • Sumeet
    Sumeet about 6 years
    Thank you! It was really helpful.
  • 5xum
    5xum about 6 years
    @SumeetSingh Happy to help.