Question

Without adding fimd the sum of 1+3+5+7+9+11+13+15+17+19+21
PLS I HAVE EXAM TOMORROW I HAVE DOUBT IN THIS PLS HELP ME​

Answer 1

Answer:

It is in arithmetic progression.

Use the formula Sn=n/2(2a+(n-1)d)

Answer 2

Question :

Find the value of -

1 + 3 + 5 + 7 + 9 + 11 + 17 + 19 + 21

Solution :

First , carefully notice that the numbers which are being added are consecutive odd numbers .

Assume that the numbers are of the form 2k + 1 ∃ 1 ≤ k ≤ 10

So, this sum can be written as :

Σ [ k = 1 to 10 ] { 2k + 1 }

=> Σ [ k = 1 to 10 ] { 2k } + Σ [ k = 1 to 10 ] { 1 }

=> 2 Σ [ k = 1 to 10 ] { k } + 1 × 11

=> 2 Σ [ k = 1 to 10 ] { k } + 11

=> 2 [ 10 × 11 ]/2 + 11

=> [ 10 × 11 ] + 11

=> 110 + 11

=> 121

Shortcut :

For sum of n odd numbers , Σ ( n ) = n²

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