Question

Find the sum of the following series 2^2+3^2+....+20^2

Answer 1

Answer:

Step-by-step explanation:

We have,

2²+3²+4²+..........20²

Now this sequence 2,3,4.......20 is in an AP with as many as 19 terms in it

For sum of squares of numbers in AP is given by

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

Where n is no of terms

Sum of terms will be

2+3+4+......20

From AP formula sum of the terms will be

(n/2)*(2a+(n-1) d)

Where a is first term, d is common difference which is 1.

Substituting values in the formula we have

2+3+4....20=209

Now sum of sequence,

1²+2²+3²+4²....20²=2870

Now we have to subtract 1² from this result

Hence answer will be 2869