Question

If Σ n = 3, then y n =​

Answer 1

Answer:

1

Step-by-step explanation:

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Answer 2

Answer:

$\huge \color{green} \tt{ ☑verified }$

answer is 2870

it is given that, \Sigma{n}=210Σn=210

and we have to find \Sigma{n^2}Σn

2

actually \Sigma{n}Σn is general form of sum of n natural numbers.

$i.e., \Sigma{n}= \\ 1 + 2 + 3 + 4 + 5 + .... + n</p><p>$

⇒210 = n(n + 1)/2 [ sum of n natural number is n(n+1)/2 ]

⇒ 420 = n(n + 1)

⇒420 = n² + n

⇒n² + 21n - 20n - 420 = 0

⇒n(n + 21) - 20(n + 21) = 0

⇒(n - 20)(n + 21) = 0

⇒n = 20, -21

hence, there are 20 natural numbers.

$so \: now \: \Sigma{n^2}$

= 1² + 2² + 3² + 4² + .... + 20²

= 20(20 + 1)(2 × 20 + 1)/6 [ sum of square of n natural numbers is n(n + 1)(2n + 1)/6 ]

= 20 × 21 × 41/6

= 420 × 41/6

= 70 × 41

= 2870

also read similar questions: write sigma notation

8-27+64-125+...+(-1)^n n^3=