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OliviaMarius
Pe: 2014-02-01T16:36:43+02:00 In: In:

ajutati-ma va rog!!!!!

Am nevoie de ajutor la o problema

calculati urmatoarele sume

………………………………………………
S=1+3+5+….+2n-1

Si ar mai fi una

S=100 x 99 – 99 x 98 + 98 x 97 – 97 x 96 + …+4 x 3 – 3 x 2 + 2 x 1

va rog sa imi si explicati pasii
Multumesc! 😀

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3 raspunsuri

  1. tata2008
    maestru (V)

    S=100 x 99 – 99 x 98 + 98 x 97 – 97 x 96 + …+4 x 3 – 3 x 2 + 2 x 1

    \rm{\bl\\ S=\underbrace{\underbrace{100 x 99 - 99 x 98}_{\underbrace{99(100-98)}_{99\cdot2}} + \underbrace{98 x 97 - 97 x 96}_{\underbrace{97(98-96)}_{97\cdot2}}+ ...+\underbrace{4 x 3 - 3 x 2}_{\underbrace{3(4-2)}_{3\cdot2}}+ 2 x 1}_{\underbrace{2 \cdot (99+97+ ... + 3+1)}_{ 2 \cdot 50^{^2} = 5000}

  2. tata2008
    maestru (V)

    S=1+3+5+….+2n-1


    \rm{\Large\bl\\ S = 1 + 3 + 5 + .... + 2n-5 + 2n-3 + 2n-1 \\ p_1... \underline{S =2n-1+2n-3+ 2n-5+ ... + 5 + 3 + 1 }\\ p_2... 2S = \underbrace{2n + 2n + 2n + ... + 2n + 2n + 2n }_{n termeni}\\ p_3... 2S = 2n \cdot n /_{:2}\\ p_4... S = n^2 (n reprezinta numarul termenilor sumei)

  4. OliviaMarius

    Multumesc mult chiar m-a ajutatp 😀

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