hamburger menu
All Coursesall course arrow
adda247
reward-icon
adda247
    arrow
    arrow
    arrow
    The sum of the first 20 terms of the series 15×6+16×7+17×8+...\frac{1}{5×6}+\frac{1}{6×7}+\frac{1}{7×8}+...5×61​+6×71​+7×81​+...​ is:
    Question

    The sum of the first 20 terms of the series 15×6+16×7+17×8+...\frac{1}{5×6}+\frac{1}{6×7}+\frac{1}{7×8}+...​ is:

    A.

    1.6

    B.

    16

    C.

    0.016

    D.

    0.16

    Correct option is D

    Given:

    15×6+16×7+17×8+...\frac{1}{5×6}+\frac{1}{6×7}+\frac{1}{7×8}+...

    Concept Used:

    Each term in the series can be rewritten as:

    1n(n+1)=1n1n+1\frac{1}{n(n+1)} = \frac{1}{n} - \frac{1}{n+1}​​

    Solution:

    15×6+16×7+17×8+...\frac{1}{5×6}+\frac{1}{6×7}+\frac{1}{7×8}+...

    (1516)+(1617)+(1718)++(124125)\left( \frac{1}{5} - \frac{1}{6} \right) + \left( \frac{1}{6} - \frac{1}{7} \right) + \left( \frac{1}{7} - \frac{1}{8} \right) + \dots + \left( \frac{1}{24} - \frac{1}{25} \right)​​

    That most terms cancel out:

    15125\frac{1}{5} - \frac{1}{25}

    5125\frac{5-1}{25}

    425\frac{4}{25}

    = 0.16

    Thus, the correct answer is (d).

    Free Tests

    Free
    Must Attempt

    RRB NTPC UG Level PYP (Held on 7 Aug 2025 S1)

    languageIcon English
    • pdpQsnIcon100 Questions
    • pdpsheetsIcon100 Marks
    • timerIcon90 Mins
    languageIcon English
    Free
    Must Attempt

    CBT-1 Full Mock Test 1

    languageIcon English
    • pdpQsnIcon100 Questions
    • pdpsheetsIcon100 Marks
    • timerIcon90 Mins
    languageIcon English
    Free
    Must Attempt

    RRB Group D Full Mock Test 1

    languageIcon English
    • pdpQsnIcon100 Questions
    • pdpsheetsIcon100 Marks
    • timerIcon90 Mins
    languageIcon English
    test-prime-package

    Access ‘RRB NTPC’ Mock Tests with

    • 60000+ Mocks and Previous Year Papers
    • Unlimited Re-Attempts
    • Personalised Report Card
    • 500% Refund on Final Selection
    • Largest Community
    students-icon
    446k+ students have already unlocked exclusive benefits with Test Prime!
    Our Plans
    Monthsup-arrow