Statement 1 :
The sum of the series 1+(1+2+4)+(4+6+9)+(9+12+16)+….+(361 +380 +400) is 8000
Statement 1:
`underset(k=1)overset(n)Sigma (k^3-(k-1)^3)=n^3`, for any natural number n.

Statement 1 : The sum of the series 1+(1+2+4)+(4+6+9)+(9+12+16)+….+(361 +380 +400) is 8000 Statement 1: Sigma_(k=1)^(n) (k^3-(k-1)^3)=n^3 , for any natural number n.

prove that 1+5+9+ . . .+(4n-3)=n(2n-1), for all natural number n.

Statement 1: The sum of the series 1""+""(1""+""2""+""4)""+""(4""+""6""+""9)""+""(9""+""12""+""16)""+"". . . . . . +""(361""+""380""+""400)"" i s ""8000 . Statement 2: sum_(k=1)^n(k^3-(k-1)^3)=n^3 for any natural number n. (1) Statement 1 is false, statement 2 is true (2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 (3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1 (4) Statement 1 is true, statement 2 is false

If underset(k=0)overset(n)(sum)(k^(2)+k+1)k! =(2007).2007! , then value of n is

The sum, underset(n-1)overset(10)(Sigma)(n(2n+1)(2n-1))/5 is equal to.........

Sum of n terms of the series 1/(1.2.3.4.)+1/(2.3.4.5) +1/(3.4.5.6)+....

Sum of n terms of the series 1/(1.2.3.4.)+1/(2.3.4.5) +1/(3.4.5.6)+....

The value of cot (underset(n=1)overset(23)sum cot^(-1) (1 + underset(k=1)overset(n)sum 2k)) is

Statement 1: 1 is a natural number. Statement 2: (n^(5))/(5)+(n^(3))/(3)+(6n)/(15) is a natural number for all n in NN .

Evaluate : sum_(k=1)^n (2^k+3^(k-1))