PYQ Vault
EbooksTutor

Sum of f(k/n) using f(x) + f(a - x) = constant

This type of question, asked 5 times: 2021 Paper 4, 27 Jun 2022, 24 Jan 2023, 24 Jan 2025, 28 Jan 2025. All 5 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 4

    74
    A function f(x)f(x) is given by f(x)=5x5x+5f(x) =\frac{5^{x}}{5^{x}+ 5}, then the sum of the series f(120)+f(220)+f(320)+……+f(3920)f\left( \frac{1}{20} \right)+f\left( \frac{2}{20} \right)+f\left( \frac{3}{20} \right)+ \ldots\ldots +f\left( \frac{39}{20} \right) is equal to:

    Tap an option to check your answer.

  2. Question 2

    27 Jun 2022

    81
    Let f:R→Rf:R\rightarrow R be a function defined f(x)=2e2xe2x+ef(x) =\frac{2e^{2x}}{e^{2x}+e}. Then f(1100)+f(2100)+f(3100)+…..+f(99100)f\left( \frac{1}{100} \right)+f\left( \frac{2}{100} \right)+f\left( \frac{3}{100} \right)+ \ldots.. +f\left( \frac{99}{100} \right) is equal to

  3. Question 3

    24 Jan 2023

    153
    If f(x)=22x22x+2, x∈Rf(x)=\frac{2^{2x}}{2^{2x}+2},\ x\in R, then f(12023)+f(22023)+⋯+f(20222023)f\left(\frac{1}{2023}\right)+f\left(\frac{2}{2023}\right)+\cdots+f\left(\frac{2022}{2023}\right) is equal to

    Tap an option to check your answer.

  4. Question 4

    24 Jan 2025

    55
    Let f(x)=2x+2+1622x+1+2x+4+32f(x) =\frac{2^{x + 2}+ 16}{2^{2x + 1}+2^{x + 4}+ 32}. Then the value 8(f(115)+f(215)+…+f(5915))8\left( f\left( \frac{1}{15} \right)+ f\left( \frac{2}{15} \right)+ \ldots + f\left( \frac{59}{15} \right) \right) is equal to

    Tap an option to check your answer.

  5. Question 5

    28 Jan 2025

    54
    If f(x)=2x2x+2,x∈Rf(x) =\frac{2^{x}}{2^{x}+\sqrt{2}},x \in R, then ∑k=181f(k82)\sum_{k = 1}^{81} f\left( \frac{k}{82} \right) is equal to :

    Tap an option to check your answer.