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Sequences and Series — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSequences and Series1 Mark
MCQ
Find the sum of series $6^3+ 7^3+…..…..+ 20^3$.
  • ✓
    $43875$
  • B
    $83775$
  • C
    $43775$
  • D
    $43975$
✓

Answer

Correct option: A.
$43875$
$6^3+ 7^3+………..+ 20^3$
$= (1^3+ 2^3+ 3^3+……..+ 20^3) – (1^3+ 2^3+ 3^3+ 4^3+ 5^3)$
$=\Big(\frac{20\times21}{2}\Big)^2-\Big(\frac{5\times6}{2}\Big)^2$
$=(210)^2-(15)^2$
$=225\times195$
$=43875$

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