Question

Sum the series 1square+(1square+2square)+(1square+2square+3square)+.....

Answer 1

Answer:

∑Un  = n(n+1)²(n+2)/12

Step-by-step explanation:

​ Un = the nth term = ∑n² =  n(n+1)(2n+1)/6 , last term

we want to sum up the above term from 1 to n

therefore ;

∑Un = ∑n(n+1)(2n+1)/6 = 1/6  ∑n(n+1)(2n+1) = 1/6  ∑(2n³ + 3n² + n

 ∑Un = 1/6 { ∑ 2n³ + ∑ 3n²  + ∑n }

 ∑Un = 1/6 {  n²(n+1)²/2 +  n(n+1)(2n+1)/2  +  n(n+1)/2 }

   ∑Un  = n(n+1)/12 {  n²+n + 2n+2}

∑Un  = n(n+1)/12 {  n²+3n +2}

∑Un  = n(n+1)²(n+2)/12

 

Answer 2

Answer:

how can you call each term a sq