Question

Express the following sums using sigma notation.a. 1 plus 3 plus 5 plus 7 plus ... plus 99b. 8 plus 11 plus 14 plus ... plus 32c. 6 plus 10 plus 14 plus ... plus 54d. StartFraction 1 Over 1 times 4 EndFraction plus StartFraction 1 Over 2 times 5 EndFraction plus StartFraction 1 Over 3 times 6 EndFraction plus ... plus StartFraction 1 Over 49 times 52 EndFraction

Answer 1

Answer:

e following sums using sigma notation.a. 1 plus 3 plus 5 plus 7 plus ... plus 99b. 8 plus 11 plus 14 plus ... plus 32c. 6 plus 10 plus 14 plus ... plus 54d. StartFraction 1 Over 1 times 4 EndFraction plus StartFraction 1 Over 2 times 5 EndFraction plus StartFraction 1 Over 3 times 6 EndFraction plus ... plus StartFraction 1 Over 49 times 52 EndFraction add them

Step-by-step explanation:

Answer 2

Answer:

a. $1+3+5+7+...+99$ = Σ $\left \{ {{\infty} \atop {n=1}} \right.$$2n+1$,  n∈Z

b. $8+11+14+...+32$ = Σ $\left \{ {{\infty} \atop {n=1}} \right.$ $3n+5$, n∈Z

c. $6+10+14+...+54$ = Σ $\left \{ {{\infty} \atop {n=1}} \right.$ $4n+2$, n∈Z

d. $\frac{1}{(1)*(4)}+\frac{1}{(2)*(5)}+\frac{1}{(3)*(6)}+...+\frac{1}{(49)*(52)}$ = Σ $\left \{ {{\infty} \atop {n=1}} \right.$ $\frac{1}{(n)(n+3)}$, n∈Z

Step-by-step explanation:

So basically you only need to find a possible sequence which represent those list of numbers. Once you have done that you only need to express it as a sum.

You can find more information in the next link:

https://www.mathsisfun.com/algebra/sequences-series.html