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    Method of Difference - Practice Questions & MCQ

    Updated on Sep 18, 2023 18:34 AM

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    • 11 Questions around this concept.

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    QuestionMEDIUM

    The sum of the series

    \frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{3.4}-........upto\: \infty

    is equal to:

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    If $t_n$ denotes the $n^{\text {th }}$ term of the series $2+3+6+11+18+\ldots$ then $t_{50}$ is

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    The sum of

    $(1^{2}-1+1)(1!)+(2^{2}-2+1)(2!)+...+(n^{2}-n+1)(n!)$

    is

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    Let $\mathrm{S}_{\mathrm{n}}=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\ldots$ upto n terms. If the sum of the first six terms of an A.P. with first term p and common difference p is $\sqrt{2026 \mathrm{~S}_{2025}}$, then the absolute difference between $20^{\text {th }}$ and $15^{\text {th }}$ terms of the A.P. is

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    The value of $\lim _{n \rightarrow \infty}\left(\sum_{K=1}^n \frac{k^3+6 k^2+11 k+5}{(k+3)!}\right)$ is:

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    Concepts Covered - 1

    METHOD OF DIFFERENCES (Shortcut)

    METHOD OF DIFFERENCES (Shortcut)

    To find the $\mathrm{n}^{\text {th }}$ term of the series, you can use the following steps:
    If the sequence of the first consecutive difference is in A.P., then the $n^{\text {th }}$ term, $T_n=a n^2+b n+c$ or $a(n-1)(n-2)+b(n-1)+c$, where $a, b$ and $c$ are constants. To find the value of $a, b$ and $c$ put $n=1,2,3$ and put the value of $T_1, T_2, T_3$.

    If the sequence of the first consecutive difference is in G.P., then the $n$th term, $T_n=a r^n+b$, where $a$ and $b$ are constant terms and $r$ is the common ratio of GP. To find the value of $a$ and $b$ put $n=1,2$ and put the value of $T_1, T_2$

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    METHOD OF DIFFERENCES (Shortcut)

    Study other Related Concepts

    Method of Difference Current Topic

    Sequence And Series
    Arithmetic Progression
    Sum of n Terms of an AP
    Arithmetic Mean in AP
    Geometric Progression
    Geometric Mean In GP
    Sum To n Terms Of a GP
    Harmonic Progression
    Harmonic Mean in HP
    Relation between A.M., G.M. and H.M.

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    Books

    Reference Books

    METHOD OF DIFFERENCES (Shortcut)

    Mathematics for Joint Entrance Examination JEE (Advanced) : Algebra

    Page No. : 5.26

    Line : 41

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