\sum_{k=1}^{n} K : {n(n+1)}/2 : : \sum_{k=1}^{n} K^2 : .........

Correct Answer is : n(n+1)(2n+1)6

TS ICET 23 May 2018 Shift 1 Paper

Note: The following question lias a sequence of numbers or letters that follow a definite pattern is given. Each question has a blank space. This has to be filled by the correct answer from the four given options to complete the sequence without breaking the pattern

Question : 29 of 200

Marks: +1, -0

∑↙{k=1}↖n K : {n(n+1)}/2

: :

∑↙{k=1}↖n K^2

: ......

...

${n^2(n+1)^2}/4$
${n(n+1)(n+2)}/6$
${(n+1)^2(n+2)^2}/4$
${n(n+1)(2n+1)}/6$

Validate

Solution:

∑_{k=1}^n

is related to

{n(n+1)}/2⇒

sum of n natural numbers
Similarly

∑_{k=1}^nK^2

is related to

{n(n+1)(2n+1)}/6

⇒ Sum of the squares of the first n natural numbers.

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