Question

The series 10° +2k
+3k+2
is convergent, then the value of k can be​

Answer 1

Answer:

10°+2k+3k+2

=10°+5k+2

Answer 2

k=2

Convergence

A series converges if the sequence of partial sums converges to s.

∞

Σ$a_{n}$$= \lim_{k \to \infty} s_k =s$

n=1

• Series are both convergent or divergent.
• 10^0+2k+3k+2
• 10^0+5k+2

∞

∑= $\frac{2^{k} }{3^{k} } +(1-1)$

k=1

 ∞

=[∑($(\frac{2}{3} )^{k}$]-1

k=0

  ∞

=[∑ $(\frac{2}{3}) ^{k-1}$]-1

k=1

=$\frac{1}{1-\frac{2}{3} }-1$

k=2