Question

The value of Sigma 18+sigma 19 is
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Answer 1

Answer:

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Answer 2

Given :   ∑18   ,  ∑19

To find : Sum of both

Solution:

∑18   + ∑19

∑n  = n(n + 1)/2

∑18 = 18(18 + 1)/2  , ∑19 = 19(19 + 1)/2

= 18(18 + 1)/2  +  19(19 + 1)/2

= 18(19)/2  + 19(20)/2

= (19/2) (18 + 20)

= (19/2)(38)

= 19 (19)

= 19²

= 361

∑18   + ∑19 =  361

also we can  conclude that    ∑n   + ∑(n+1)   = (n+ 1)²

n(n + 1)/2  + (n+1)(n + 2)/2

= ((n + 1)/2 ) ( n + n + 2)

= ((n+1)/)(2n + 2)

= (n + 1)(n + 1)

= (n + 1)²

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